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! CONTEMPORARY MATHEMATICS
162
Classification of Algebraic Varieties
Algebraic Geometry Conference on Classification of Algebraic Varieties
May 22-30, 1992 University of L' Aquila
L' Aquila , Italy
Ciro Ciliberto E. Laura Livorni
Andrew J. Sommese Editors
Recent Titles in This Series
162 Ciro Ciliberto, E. Laura Livomi, and Andrew J. Sommese, Editors, Classification of algebraic varieties, 1994
161 Paul A. Schweitzer, S. J., Steven Hurder, Nathan Moreira dos Santos, and Jose Luis Arraut, Editors, Differential topology, foliations, and group actions, 1994
160 Niky Kamran and Peter J. Olver, Editors, Lie algebras, cohomology, and new applications to quantum mechanics, 1994
159 William J. Heinzer, Craig L. Huneke, and Judith D. Sally, Editors, Commutative algebra: Syzygies, multiplicities, and birational algebra, 1994
158 Eric M. Friedlander and Mark E. Mahowald, Editors, Topology and representation theory, 1994
157 Alfio Quarteroni, Jacques Periaux, Yuri A. Kuznetsov, and Olof B. Widlund, Editors, Domain decomposition methods in science and engineering, 1994
156 Steven R. Givant, The structure of relation algebras generated by relativizations, 1994 155 William B. Jacob, Tsit-Yuen Lam, and Robert 0. Robson, Editors, Recent advances in
real algebraic geometry and quadratic forms, 1994 154 Michael Eastwood, Joseph Wolf, and Roger Zierau, Editors, The Penrose transform and
analytic cohomology in representation theory, 1993 153 RichardS. Elman, Murray M. Schacher, and V. S. Varadarajan, Editors, Linear algebraic
groups and their representations, 1993 152 Christopher K. McCord, Editor, Nielsen theory and dynamical systems, 1993 151 Matatyahu Rubin, The reconstruction of trees from their automorphism groups, 1993 150 Carl-Friedrich Bodigheimer and Richard M. Hain, Editors, Mapping class groups and
moduli spaces of Riemann surfaces, 1993 149 Harry Cohn, Editor, Doeblin and modem probability, 1993 148 Jeffrey Fox and Peter Haskell, Editors, Index theory and operator algebras, 1993 147 Neil Robertson and Paul Seymour, Editors, Graph structure theory, 1993 146 Martin C. Tangora, Editor, Algebraic topology, 1993 145 Jeffrey Adams, Rebecca Herb, Stephen Kudla, Jian-Shu Li, Ron Lipsman, and Jonathan
Rosenberg, Editors, Representation theory of groups and algebras, 1993 144 Bor-Luh Lin and William B. Johnson, Editors, Banach spaces, 1993 143 Marvin Knopp and Mark Sheingorn, Editors, A tribute to Emil Grosswald: Number
theory and related analysis, 1993 142 Chung-Chun Yang and Sheng Gong, Editors, Several complex variables in China, 1993 141 A. Y. Cheer and C. P. van Dam, Editors, Fluid dynamics in biology, 1993 140 Eric L. Grinberg, Editor, Geometric analysis, 1992 139 Vinay Deodhar, Editor, Kazhdan-Lusztig theory and related topics, 1992 138 Donald St. P. Richards, Editor, Hypergeometric functions on domains of positivity, Jack
polynomials, and applications, 1992 137 Alexander Nagel and Edgar Lee Stout, Editors, The Madison symposium on complex
analysis, 1992 136 Ron Donagi, Editor, Curves, Jacobians, and Abelian varieties, 1992 135 Peter Walters, Editor, Symbolic dynamics and its applications, 1992 134 Murray Gerstenhaber and Jim Stasheff, Editors, Deformation theory and quantum
groups with applications to mathematical physics, 1992 133 Alan Adolphson, Steven Sperber, and Marvin Tretkoff, Editors, p-Adic methods in
number theory and algebraic geometry, 1992 132 Mark Gotay, Jerrold Marsden, and Vincent Moncrief, Editors, Mathematical aspects of
classical field theory, 1992
(Continued in the back of this publication)
http://dx.doi.org/10.1090/conm/162
CoNTEMPORARY MATHEMATICS
162
Classification of Algebraic Varieties Algebraic Geometry Conference on Classification of Algebraic Varieties
May 22-30, 1992 University of L' Aquila
L' Aquila, Italy
Ciro Ciliberto E. Laura Livorni
Andrew J. Sommese Editors
American Mathematical Society Providence, Rhode Island
EDITORIAL BOARD Craig Huneke, managing editor
Clark Robinson J. T. Stafford Linda Preiss Rothschild Peter M. Winkler
The Algebraic Geometry Conference on Classification of Algebraic Varieties was held May 22-30, 1992, at the University of L'Aquila, L'Aquila, Italy, with support provided by the following institutions: Ambasciata di Spagna; Azienda Autonoma del Soggiorno e Turismo di L'Aquila; Comune di L'Aquila; C.N.R. (Consiglio Nazionale delle Ricerche); Consiglio Regionale di L'Aquila; Dipartimento di Matematica dell'Universita degli Studi di L'Aquila; Dipartimento di Matematica dell'Universita degli Studi di Pisa; Dipartimento di Matematica dell'Universita degli Studi di Roma II; Fondazione Cassa di Risparmio della Provincia di L'Aquila; G.N.S.A.G.A (Gruppo Nazionale perle Strutture Algebriche e Geometriche e loro Applicazioni); Universita degli Studi di L' Aquila.
1991 Mathematics Subject Classification. Primary 14-06.
Library of Congress Cataloging-in-Publication Data Algebraic Geometry Conference on Classification of Algebraic Varieties (1992: University of L'Aquila)
Classification of algebraic varieties: proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, May 22-30, 1992, University ofL'Aquila, L'Aquila, ltaly/Ciro Ciliberto, E. Laura Livorni, Andrew J. Sommese, editors.
p. em. -(Contemporary mathematics; v. 162) ISBN 0-8218-5179-9 (acid-free) 1. Algebraic varieties-Classification-Congresses. I. Ciliberto, D. (Ciro), 1950-. II. Livorni,
E. L. (Elvira Laura), 1951-. III. Sommese, Andrew John. IV. Title. V. Series: Contemporary mathematics (American Mathematical Society); . QA564.A37 1992 516.3'5-dc20
93-44549 CIP
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Contents
Introduction 1x
List of Participants xi
List of Seminars XlX
On curves in C(2) generating proper abelian subvarieties of J(C) A. ALZATI AND G. PIROLA 1
Lefschetz type results for proper intersections L. BADESCU 19
Some effects of the spectral values on reductions M. C. BELTRAMETTI AND A. J. SOMMESE 31
Surfaces in P4 and deficiency modules G. BOLONDI 49
The class C is not stable by small deformations. II F. CAMPANA 65
Surfaces with K 2 = x = 2 and special nets of quadrics in 3-space F. CATANESE, P. CRAGNOLINI, AND P. OLIVERIO 77
Non-isomorphic curves of genus four with isomorphic (non-polarized) jaco-bians
C. CILIBERTO AND G. VAN DER GEER 129
Deformations of symmetric products of curves B. FANTECHI 135
Q-acyclic surfaces and their deformations H. FLENNER AND M. ZAIDENBERG 143
On a question of J. Kollar A. GRASSI 209
Boundedness for some special families of embedded manifolds P. lONESCU AND M. TOMA 215
Generalized Euler sequence and toric varieties K. J ACZEWSKI 227
vii
viii CONTENTS
A generalized Teissier-Plucker formula S. L. KLEIMAN 249
Log surfaces of general type; some conjectures J. KOLLAR 261
On triple covers of pn as very ample divisors A. LANTER!, M. PALLESCHI, AND A. J. SOMMESE 277
Component numbers for torsion sections of semistable elliptic surfaces R. MIRANDA 293
Braid group techniques in complex geometry III: Projective degeneration of v3
B. MOISHEZON AND M. TEICHER 313
Braid group techniques in complex geometry IV: Braid monodromy of the branch curve 83 of V3 --+ CIP'2 and application to TI1 (CIP'2 - 83 , *)
B. MOISHEZON AND M. TEICHER 333
On the irregularity of cyclic coverings of the projective plane F. SAKAI 359
Counting rational points on cubic surfaces SIR P. SWINNERTON-DYER 371
Miyaoka-Yau inequality for normal surfaces and local analogues J. WAHL 381
Minimal models of Calabi-Yau threefolds P. M. H. WILSON 403
Introduction
The vitality of algebraic geometry belies its long history and great depth. This
is because of the ongoing wide ranging, interaction that algebraic geometry has with
the rest of mathematics.
This activity, was clear at the L'Aquila Conference, which was attended by
numerous mathematicians from all the word (see enclosed list of participants) and is
illustrated by the breadth of the problems treated in the seminars (see also the
enclosed list of seminars held during the Conference) and studied in the proceedings.
Just to mention a few of the topics in the proceedings, there are articles on:
• the topology of algebraic varieties and on braid groups,
• Riemann surfaces and their jacobians,
• projective classification theory,
• toric varieties,
• enumerative formulae,
• generalizations of Kahler differential geometry,
• the theory of algebraic surfaces, • the Calabi-Yau threefolds (of much current interest to physicists),
• the spectacular mathematics growing out of the work of Mori. The conference in L'Aquila was not only a place for fruitful mathematical
interaction, but was an occasion where old friendships were renewed and many new
friendships were made. The atmosphere was very stimulating and enjoyable.
The conference and this proceedings owe their great success to all who attended
for their active discussions and their endurance.
The editors
ix
List or participants
A. Alzati, Dipartimento di Matematica- Universita degli Studi di Milano - Via C.
Saldini 50 - 20133 MILANO - Italy. E-mail address: ALZATI @
UMIMAT.MAT.UNIMI.IT
M. Andreatta, Dipartimento di Matematica - Universita degli Studi di Trento -
38050 POVO - Trento - Italy. E-mail address: ANDREATTA @
TINCISCA.BITNET
E. Arbarello, Dipartimento di Matematica - Universita degli Studi di Roma I -
Piazzale Aldo Moro 5 - 00185 ROMA- Italy.
E. Arrondo, Departamento de Algebra Facultad de Matematicas - Universidad
Complutense - E 28040 MADRID - Spain. E-mail address: W 258 @
EMDUCM11.BI1NET
L. Blldescu, Institute of Mathematics of the Romania Academy- P.O. BOX 1-764,
Ro-70700- BUCHAREST- Romania
E. Ballico, Dipartimento di Matematica- Universita degli Studi di Trento - 38050
POVO - Trento - Italy. Fax number 0039-461881624. E-mail address:
BALLICO@ I1NCISCA. BI1NET
F. Bardelli, Dipartimento di Matematica - Universita degli Studi di Pisa - Via
Buonarroti 2 - 56127 PISA - Italy. E-mail address: BARDELL! @
DM.UNIPI.IT
M. A. Barja, Departamento Matematica Aplicada 1 - Etseib Universitat Politecnia
Catalunya- Diagonal647- BARCELONA- Spain.
I. Bauer, Dipartimento di Matematica - Universita degli Studi di Pisa - Via
Buonarroti 2 - 56127 PISA - Italy. E-mail address: BAUER @
BIANCHI.DM.UNIPI.IT
S. Bauer, Mathematisches Institut der UniversiUit - Universitat Gottingen -
Bunsenstrasse 3 - 5 - 3400 GOTTINGEN - Germany. E-mail address: BAUER
@ CFGAUSS. UNIMATH.GWDG.DE
xi
xii LIST OF PARTICIPANTS
M. C. Beltrametti, Dipartimento di Matematica - Universita degli Studi di
Genova - Via L. B. Alberti 4 - 16132 GENOVA - Italy. E-mail address:
MBELTRA@ IGECUNIV. CISI.UNIGE.IT
L. Berardi, Dipartimento di Energetica- Universita degli Studi di L'Aquila- 67100
L'AQUILA - Italy
M. Bertolini, Dipartimento di Matematica - Universita degli Studi di Milano - Via
C. Saldini 50 - 20133 MILANO - Italy. E-mail address: BERTOLINI @
UMIMAT.MAT.UNIMI.IT
G. M. Besana, Dipartimento di Matematica- Universita degli Studi di L'Aquila -
Via Vetoio, Loc. Coppito - 67100 L'AQUILA - Italy. E-mail address:
BESANA@ VXSCAQ.CINECA.IT
A. Biancofiore, Dipartimento di Matematica- Universita degli Studi di L'Aquila-
Via Vetoio, Loc. Coppito - 67100 L'AQUILA - Italy. E-mail address:
BIANCOFIORE@ VXSCAQ.CINECA.IT
G. Bolondi, Dipartimento di Matematica- Universita degli Studi di Trento - 38050
POVO- Trento- Italy. E-mail address: BOLONDI@ ITNCISCA.BITNET
G. Brown, Mathematics Institute- University of Warwick- COVENTRY CV4 7AL
-England E-mail address: GDB@ MATHS.WARWICK.AC.UK
A. Bruno, Dipartimento di Matematica- Universita degli Studi di Roma 1- Piazzale
Aldo Moro 5-00185 ROMA- Italy
F. Campana, Department de Mathematiques- Universite Nancy 1 - BP 239, 54506
V ANDOEIVRE CEDEX- France.E-mail address: CAMPANA@ IECH.FR
G. Casnati, Dipartimento di Matematica Pura ed Applicata- Universita di Padova-
Via Belzoni 7 - 35131 PADOVA - Italy. E-mail address: CASNATI@
PDMATl.UNIPD.IT
F. Catanese, Dipartimento di Matematica - Universita degli Studi di Pisa - Via
Buonarroti 2 - 56127 PISA - Italy. E-mail address: CATANESE @
ICNUVEVM.BITNET
C. Ciliberto, Dipartimento di Matematica-Universita degli Studi di Roma II- Via
della Ricerca Scientifica- 00133 ROMA -Italy. E-mail address: CILIBERTO
@ MAT.UTOVRM.IT
LIST OF PARTICIPANTS xiii
E. Colombo, Dipartimento di Matematica - Universita degli Studi di Milano - Via
C. Saldini 50 - 20133 MILANO - Italy. E-mail address: COLOMBO@
UMIMAT.MAT.UNIMI.IT
M. Cornalba, Dipartimento di Matematica- Universita degli Studi di Pavia- Strada
Nuova 65 - 27100 PAVIA - Italy. E-mail address: CORNALBA @
IPV85.UNIPV.IT
A. Corti, Scuola Normale Superiore di Pisa- Piazza dei Cavalieri 7 - 56127 PISA-
Italy. E-mail address: CORTI@ IPISNSVA.BI1NET
M. de Cataldo, Department of Mathematics - University of Notre Dame - Notre
Dame, Indiana 46556 - U.S.A. E-mail address: MARKAN @
CART AN.MATH.ND.EDU
S. Di Rocco, Department of Mathematics - University of Notre Dame - Notre
Dame, Indiana 46556 - U.S.A. E-mail address: SANDRADR @
CARTAN.MATH. ND.EDU
I. Dolgachev, Department of Mathematics - University of Michigan - ANN
ARBOR, MI 48109 - U.S.A. E-mail address: IGOR_DOLGACHEV @
UM.UMICH.EDU
L. Ein, Department of Mathematics - University of Illinois at Chicago -
CHICAGO, IL 60680- U.S.A.
G. Ellingsrud, Matematisk Institutt - Universitet i Bergen - Allegaten 55 - 5007
BERGEN -Norway. E-mail address: GEIR@ MI.UIB.NO
F. Eugeni, Dipartimento di Energetica- Universita degli Studi di L'Aquila - 67100
L'AQUILA - Italy
M. L. Fania, Dipartimento di Matematica- Universita degli Studi di L'Aquila- Via
Vetoio, Loc. Coppito- 67100 L'AQUILA- Italy. E-mail address: FANIA@
VXSCAQ. CINECA.IT
B. Fantechi, Dipartimento di Matematica - Universita degli Studi di Trento - 38050
POVO- Trento- Italy. E-mail address: FAN1ECHI@ ITNCISCA.BI1NET
H. Flenner, Mathematisches Institut der Universitlit - Universitlit Gottingen -
Bunsenstrasse 3- 5 - 3400 GOTTINGEN - Germany. E-mail address:
HFLENNER@ CFGAUSS. UNI-MATH.GUDG.DE
xiv LIST OF PARTICIPANTS
P. Francia, Dipartimento di Matematica - Universita degli Studi di Genova - Via
L.B. Alberti 4 - GENOVA - Italy. E-mail address: FRANCIA @
IGECUNIV .BITNET
E. Frigerio, Dipartimento di Matematica - Universita degli Studi di Milano - Via
C. Saldini 50- 20133 MILANO- Italy
L. Guerra, Dipartimento di Matematica- Universita di Perugia - Via Vanvitelli 1 -
06100 PERUGIA- Italy
L. Gottsche, Max-Planck-Institut ftir Mathematik - Gottfried Claren Strasse 26 -
5300 BONN 3 - Germany. E-mail address: LOTHAR @ MPIM-
BONN.MPG.DBP.DE
K. Hulek, Institut ftir Mathematik- Universitat Hannover- Welfengarten 1 W 3000
HANNOVER 1 - Germany. E-mail address: [email protected].
MA THEMATIK.UNI-HANNOVER.DBP.DE
P. Ionescu, Department of Mathematics -University of Bucharest -
St.ACADEMIEI, NR. 14- 70109 BUCHAREST- Romania
V. Iskovskih, Steklov Mathematician Institute- Vivilov Str. 42 - MOSCOW -
GSP 1.11 7 966 - RUSSIA
K. Jaczewski, Institute of Mathematics - Warsaw University - Banache 2 - 02-097
WARSZAWA- Poland. E-mail address: MAS 1@ PLEARN.BITNET
T. Kato, Katholieke Universiteit Leuven-Department of Mathematics-fac. of Sci. -
Yamaguchi University- YAMAGUCHI 753- JAPAN
Y. Kawamata, Department of Mathematics - University of Tokyo - Hongo
TOKYO 113 - Japan. E-mail address: KAWAMATA @ UTSS.S.U-
TOKYO.AC.JP
S. L. Kleiman, Department of Mathematics - 2-278 MIT - CAMBRIDGE -
Massachusetts 02139- U.S.A. E-mail address: KLEIMAN@ MATH. MIT.
EDU
J. Kollar, Department of Mathematics- University of Utah- SALT LAKE CITY-
UT 84112- U.S.A. E-mail address: Kollar@ MATH.UTAH.EDU
LIST OF PARTICIPANTS XV
K. Konno, College of General Education, Kyushu University, Ropponmatsu,
Chuo-ku, FUKUOKA 810, Japan. E-mail address: KONNO @
EMMY.DM.UNIP.IT
H. H. Lange, Mathematische Institut- University of Erlangen - Bismarckstr. 1 1/2
- 8520 ERLANGEN - Germany. E-mail address: LANGE @
CNVE.RRZE.UNI-ERLANGEN. DBP.DE
A. Lanteri, Dipartimento di Matematica - Universita degli Studi di Milano - Via C.
Saldini 50 - 20133 MILANO - Italy. E-mail address: LANTER! @
UMIMAT.MAT.UNIMI.IT
E. L. Livorni, Dipartimento di Matematica- Universita degli Studi di L'Aquila -
Via Vetoio, Loc. Coppito-67100 L'AQUILA-Italy. E-mail address:LIVORNI
@ VXSCAQ. CINECA.IT
A. Lopez, Dipartimento di Matematica - Universita degli Studi di Pavia - Strada
Nuova 65 - 27100 PAVIA- Italy. E-mail address: LOPEZ@ IPVIAN.BITNET
M. Manetti, Scuola Normale Superiore di Pisa- Piazza dei Cavalieri- 56126 PISA
-Italy. E-mail address: MANEm@ IPISNSV A.BITNET
N. Manolache, Institute of Mathematics of the Romania Academy- P.O. BOX 1-
764, Ro-70700 - BUCHAREST- Romania
G. Marini, Dipartimento di Matematica- Dottorato di Ricerca - Universita degli
Studi di Roma I - Piazzale Aldo Moro 5 - 00185 ROMA - Italy. E-mail
address: MARINI@ V AXRMA. INFN.IT G. Martens, Mathematisches Institut - University of Erlangen- Niirnberg -
Bismarckstr. 1 1/2 - 8520 ERLANGEN - Germany. E-mail address:
MARTENS@ CNVE.RRZE. UNI-ERLANGEN.DBP.DE
G. Megyesi, Trinity College Cambridge- CB2 ITQ- England. E-mail address: 9M
115 @ PHX.CAM.AC.UK.
K. Meeyoung, Department of Mathematics - University of Notre Dame - Notre
Dame, Indiana 46556 - U.S.A. E-mail address: MYING @
CARTAN.MATH.ND.EDU
xvi LIST OF PARTICIPANTS
R. Miranda, Department of Mathematics - Colorado State University - FORT
COLLINS, CO 80523 - U.S.A. E-mail address: MIRANDA @
RIEMANN.MATII.COLOSTATE. EDU
Y. Miyaoka, Department of Mathematics - Rikkyo University - Nishi-Ikeburo,
Toshimaku - 171 TOKYO -Japan
B. Moishezon, Department of Mathematics - Columbia University - NEW YORK,
N.Y. 10027 -U.S.A.
J. Murre, Department of Mathematics- University of Leiden -P.O. BOX 9512-
2300 RA LEIDEN - The Netherlands. E-mail address: MURRE @
RULCRI.LEIDENUNIV .NL
K. O'Grady, Institute for Advanced Study- Princeton- New Jersey 08540- U.S.A.
P. Oliverio, Dipartimento di Matematica - Universita della Calabria - 87036
ARCA V ACAT A DI RENDE (Cosenza) - Italy
C. Okonek, Mathematisches Institut - Universitlit Ziirich - Ramistrasse 74 - CH-
8001 Zurich- Switzerland
G. Ottaviani, Dipartimento di Matematica Applicata - Universita degli Studi di
Firenze- ViaS. Marta 3- 50139 Firenze- Italy.
M. Palleschi, Dipartimento di Matematica - Universita degli Studi di Milano - Via
C. Saldini 50 - 20133 MILANO - Italy. E-mail address: APELLES @
UMIMAT.MAT.UNIMI.IT
C. Pedrini,Dipartimento di Matematica - Universita degli Studi di Genova - Via
L.B. Alberti 4 - GENOVA - Italy. E-mail address: PEDRINI @
IGECUNIV.BTINET
T. Peternell, Mathematisches Institut - Universitlit Bayreuth- Universitlitsstr. 30,
Postf. 10 12 51 - 8580 BAYREUTH - Germany. E-mail address: THOMAS.
PETERNELL@ UNI-BA YREUTH.DBP.DE
R. Piene, Matematisk Institutt - University of Oslo - P.B. 1053 Blindern - 0136
OSLO- Norway. E-mail address: RAGNIP@ MATH.uio.no
G. Pirola, Dipartimento di Matematica - Universita degli Studi di Pavia - Strada
Nuova 65 - 27100 PAVIA - Italy. E-mail address: PIR023 @
IPVIAN.BTINET
LIST OF PARTICIPANTS xvii
M. Reid, Mathematics Institute- University of Warwick- COVENTRY CV4 7AL-
England. E-mail address: MILES@ MATHS.W ARWICK.AC.UK
I. Reider, Department of Mathematics - University of Oklahoma-NORMAN, OK
73019 - U.S.A.
J. Roberts, Department of Mathematics- University of Minnesota- 206 Church St.
S.E. - MINNEAPOLIS - MN 55455 - U.S.A. E-mail address: ROBERTS @
S6. MA TH.UMN.EDU
E. Rogora, Dipartimento di Matematica - Universita degli Studi di Roma I -
Piazzale AldoMoro 5 -00185 ROMA- Italy. E-mail address: OOTIORAT@
ITCASPUR
M. Rossi, Dipartimento di Matematica - Universita degli Studi di Firenze - Via
Buonarroti 2- Italy. E-mail address: UDINI@ IFliDG.BITNET
F. Russo, Dipartimento di Matematica - Universita degli Studi di Milano - Via C.
Saldini 50 20133 MILANO- Italy
F. Sakai, Department of Mathematics - Faculty of Science - Saitama University -
Shimo-Okubo 255, URA W A 338 - Japan. E-mail address: FSAKAI @
RIMATH. SAITAMA-U.AC.JP
G. K. Sankaran, DPMMS 16- Mill Lane- CAMBRIDGE CB2 lSB- England. E-
mail address: GKSl@ PHX.CAM.AC.UK
M. Schneider, Mathematisches lnstitut- Universitiit Bayreuth- Universitiitsstr. 30,
Postf. 10 12 51 - 8580 BAYREUTH - Germany. E-mail address: MICHAEL.SCHNEIDER@ UNI-BA YREUTH.DE
E. Sernesi, Dipartimento di Matematica - Universita degli Studi di Roma III - Via
Corrado Segre 2 - 00146 ROMA - Italy. E-mail address: SERNESI @ ITCASPUR.BITNET
F. Serrano, Departament Algebra I Geometria- Universitat DE BARCELONA-
Gran Via 585 - 08007 BARCELONA - Spain. E-mail address: UBAAGX06 @
EBCESCAl
N. Shepherd-Barron, Department of Mathematics - University of Cambridge - 16
Mill Lane - CAMBRIDGE CB 2 IS B -England N.I.SHEPHERD-BARRON
@ PMMS.CAM. AC.UK
X VIii LIST OF PARTICIPANTS
H. Sterk, Faculteit der Wiskunde en Informatica - Universiteit van Amsterdam -
Plantage Muidergracht 24- 1018 TV AMSTERDAM- The Netherlands. E-
mail address: STERK@ FWI.UV A.NL
P. Supino, Dipartimento di Matematica - Dottorato di Ricerca - Universita degli
Studi di Roma I - Piazzale Aldo Moro 5 - 00185 ROMA - Italy. E-mail
address: SUPINO@ VAXRMA.INFN.IT
Sir P. Swinnerton-Dyer, The Dower House- Thriplow- Royston- HERTS SG8
7RJ - England
G. van der Geer, Matematisch Instituut- Universiteit van Amsterdam - Plantage
Muidergracht 24- NL 1018 TV AMSTERDAM- The Netherlands. E-mail
address: GEER@ FWI.UV A.NL
A. Verra, Dipartimento di Matematica- Universita degli Studi di Roma I- Piazzale
Aldo Moro 5 - 00185 ROMA -Italy.
H. Verrill, Department Mathematics of Cambridge 16- Mill Lane- CAMBRIDGE
CB2 ISB - England
M. Teicher, Department of Mathematics- BAR-ILAN University- Bamat- Gan-
Israel. E-mail address: TEICHER @ BIMACS
J. Wahl, Department of Mathematics- University of North Carolina- Chapel Hill-
NC 27599-3250- U.S.A. E-mail address: JW@ MATH.UNC.EDU
P.M.H. Wilson, Trinity College Cambridge - CB2 ITQ - England. E-mail address:
pmhW@ pmms.cam.ac.uk
J.A. Wisniewski, Institute of Mathematics - Warsaw University - Banacha 2 - 02-
097 W ARSZA W A- Poland. E-mail address: JAREKW@ PLEARN.BITNET
F.L. Zak, CEMI RAN - Krasikov st. 32, Moscow 117418, RUSSIA. E-mail
address: Zak@ cemi.msk.su Cl0201@ sucemi
R. Zollo, Dipartimento di Matematica - Universita degli Studi di L'Aquila - Via
Vetoio Loc. Coppito- 67100 L'AQUILA- Italy
F. Zucconi, Dipartimento di Matematica - Universita degli Studi di Pisa - Via
Buonarroti 2- 56127 PISA- Italy
List of seminars held during the conference
Marco Andreatta : Elementary contractions whose supporting divisors are Kx®L®r
Enrique Arrondo : Obstructions for embedding surfaces in codimension two
Lucian B adescu : Formal functions along zero loci of sections of ample vector
bundles and applications
Fabio Bardelli : Algebraic cycles on certain Calabi-Y au threefolds
Ingrid Bauer : Generic lemniscates of algebraic functions
Stefan Bauer : Moduli of bundles on elliptic surfaces
Gian Mario Besana : On the geometry of conic bundles arising in adjunction
theory
Giorgio Bolondi : Hilbert schemes of surfaces in p4- Liaison classes of surfaces in p4
Frederic Campana : The class 'C is not stable by small deformations
Alessio Corti : Birational models for threefolds fibered in del Pezzo surfaces
Igor Dolgachev : Ogg-Shafarevich theory of elliptic threefolds
Lawrence Ein : Some Reider-type theorem for smooth threefolds
Geir Ellingsrud : Twisted cubics on a general quintic threefold
Barbara Fantecbi : Deformations of Hilbert schemes of points of a surface Hubert Flenner : Rational surfaces in 3-folds with ample normal bundle
Lothar Gottsche : Hilbert schemes of points and formulas for contacts with linear
subspaces and trisecants
Klaus Hulek : New irregular surfaces in p4
Paltin Ionescu : Roundedness for some special families of embedded manifolds
V assilii Iskovskih : Relations among generators in 2-dimensional Cremona group
over a non-closed field
Krzysztof Jaczewski: Generalized Euler Sequence and Toric Varieties
Yujiro Kawamata: On the log flips and applications
Steven L. Kleiman : A generalized Teissier-Pliicker formula
Janos Kollar : Effective base point freeness
xix
XX LIST OF SEMINARS
Kazushiro Konno : Even canonical surfaces with small K2
Angelo Lopez : Noether-Lefschetz, space curves and mathematical instantons
Marco Manetti : Deformation equivalence of surfaces
Nicolae Manolache : Multiple structures on smooth support
Rick Miranda : Encoding number for torsion sections of elliptic surfaces
Yoichi Miyaoka : Rational curves of small degree on a Fano manifold
Boris Moishezon: Cuspidal Curves and Algebraic Surfaces
Jacob Murre : Motives and Chow groups
Kieran O'Grady : On the smooth classification of projective surfaces
Christian Okonek : On the topology of non-Kiihlerian surfaces
Giorgio Ottaviani : On the relatives of the Horrocks bundle on p5
Marino Palleschi : Double covers of pn as very ample divisors
Claudio Pedrini : 0-cycles on singular projective surfaces
Thomas Peternell : Manifolds with semi-positive curvature
Ragni Piene : Projective surfaces with small osculating spaces
Giampietro Pirola : Projections on abelian variety and applications
Miles Reid : Inductive Mori theory and applications
Igor Reider : On the Chern numbers and number of moduli of surfaces of general
type
Fumio Sakai : Remarks on the irregularity of cyclic multiple planes
Michael Schneider: Bounds for stable bundles and Weierstrass schemes
Edoardo Sernesi : Torelli type theorems
Nicholas Shepherd-Barron : Some foliations on tori
Sir Peter Swinnerton-Dyer : Diophantine problems on rational varieties
Gerard van der Geer: Reed-Muller Codes and Supersingular Curves
Alessandro Verra : Prym varieties of plane sextics
Jonathan Wahl : The Miyaoka-Yau inequality for normal surfaces and local
analogues
Peltan M.H. Wilson : Calabi-Yau three folds
Jarek Wisniewski: On Fano manifolds of dimension~ 4
Fyodor Zak : Quadratic normality and higher secant varieties
Recent Titles in This Series (Continued from the front of this publication)
131 L. A. Bokut', Yu. L. Ershov, and A. I. Kostrikin, Editors, Proceedings of the International Conference on Algebra Dedicated to the Memory of A. I. Mal'cev, Parts 1, 2, and 3, 1992
130 L. Fuchs, K. R. Goodearl, J. T. Stafford, and C. Vinsonhaler, Editors, Abelian groups and noncommutative rings, 1992
129 John R. Graef and Jack K. Hale, Editors, Oscillation and dynamics in delay equations, 1992
128 Ridgley Lange and Shengwang Wang, New approaches in spectral decomposition, 1992 127 Vladimir Oliker and Andrejs Treibergs, Editors, Geometry and nonlinear partial
differential equations, 1992 126 R. Keith Dennis, Claudio Pedrini, and Michael R. Stein, Editors, Algebraic K-theory,
commutative algebra, and algebraic geometry, 1992 125 F. Thomas Bruss, Thomas S. FeJ'IUSOD, and Stephen M. Samuels, Editors, Strategies for
sequential search and selection in real time, 1992 124 Darren Haile and James Osterburg, Editors, Azumaya algebras, actions, and modules,
1992 123 Steven L. Kleiman and Anders Thorup, Editors, Enumerative algebraic geometry, 1991 122 D. H. Sattinger, C. A. Tracy, and S. Venakides, Editors, Inverse scattering and
applications, 1991 121 Alex J. Feingold, Igor B. Frenkel, and John F. X. Ries, Spinor construction of vertex
operator algebras, triality, and E~ 1 >, 1991 120 RobertS. Doran, Editor, Selfadjoint and nonselfadjoint operator algebras and operator
theory, 1991 119 Robert A. Melter, Azriel Rosenfeld, and Prabir Bhattacharya, Editors, Vision geometry,
1991 118 Yan Shi-Jian, Wang Jiagang, and Yang Chong-chon, Editors, Probability theory and its
applications in China, 1991 117 Morton Brown, Editor, Continuum theory and dynamical systems, 1991 116 Brian Harbourue and Robert Speiser, Editors, Algebraic geometry: Sundance 1988, 1991 115 Nancy Flournoy and Robert K. Tsutakawa, Editors, Statistical multiple integration, 1991 114 Jeffrey C. Laprias and Michael J. Todd, Editors, Mathematical developments arising
from linear programming, 1990 113 Eric Grinberg and Eric Todd Quinto, Editors, Integral geometry and tomography, 1990 112 Philip J. Brown and Wayne A. FuUer, Editors, Statistical analysis of measurement error
models and applications, 1990 111 Earl S. Kramer and Spyros S. Magliveras, Editors, Finite geometries and combinatorial
designs, 1990 110 Georgia Benkart and J. Marshall Osborn, Editors, Lie algebras and related topics, 1990 109 Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang, Editors, Combinatorial group
theory, 1990 108 Melvyn S. Berger, Editor, Mathematics of nonlinear science, 1990 107 Mario Milman and Tomas Schonbek, Editors, Harmonic analysis and partial differential
equations, 1990 106 Wilfried Sieg, Editor, Logic and computation, 1990 105 Jerome Kaminker, Editor, Geometric and topological invariants of elliptic operators,
1990 104 Michael Makkai and Robert Pare, Accessible categories: The foundations of categorical
model theory, 1989
(See the AMS catalog for earlier titles)
Classification of Algebraic Varieties Ciro Ciliberto, E. Laura Livorni, and Andrew J. Sommese, Editors
This volume contains the proceedings of the Algebraic Geometry Confer-ence on Classification of Algebraic Varieties, held in May 1992 at the Univer-sity of L'Aquila in Italy. The papers discuss a wide variety of problems that illustrate interactions between algebraic geometry and other branches of math-ematics. Among the topics covered are algebraic curve theory, algebraic surface theory, the theory of minimal models, braid groups and the topology of alge-braic varieties, toric varieties, Calabi-Yau three-folds, enumerative formulas, and generalizations of Kahler differential geometry. In addition to algebraic geometers, theoretical physicists in some areas will find this book useful. The book is also suitable for an advanced graduate course in algebraic geometry, as it provides an overview of some areas of current research.
ISBN 0-8218-5179-9
9 780821 851791