Enumerative Geometry and Classical Algebraic Geometry

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Birkhauser Boston· Basel· Stuttgart

Enumerative Geometry and Classical Algebraic Geometry Patrick Le Barz, Yves Hervier, editors

1982

Birkhiiuser Boston. Basel • Stuttgart

Patrick Le Barz Universite de Nice Departement de Mathematiques Parc Valrose F-06034 Nice, France Yves Hervier Un±versite de Nice Deparement de Mathematiques Parc Valrose F-06034 Nice, France Library of Congress Cataloging in Publication Data Main entry under title: Enumerative geometry and classical algebraic geometry. (Progress in mathematics ; v. 24) 1. Geometry, Algebraic--Addresses, essays, lectures. 2. Fields, Algebraic-Addresses, essays, lectures. 3. Algebraic varieties--Addresses, essays, lectures. I. Le Barz, Patick, 1948II. Hervier, Y. III. Series: Progress in mathematics (Cambridge, Mass.) v. 24. QA564.E58 1982 516.3'5 82-17748 lSBN-13: 978-0-8176-3106-2 e-lSBN-13: 978-1-4684-6726-0 DOl: 10.1007/978-1-4684-6726-0

CIP - Kurztitelaufnahme der Deutschen Bibliothek LeBarz, Patrick: Enumerative geometry and classical algebraic geometry I Patrick Le Barz and Yves Hervier. Boston; Basel; Stuttgart : Birkh~user, 1982. (Progress in Mathematics; Vol. 24) lSBN-13: 978-0-8176-3106-2 NE: Hervier, Yves:;

GT

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission of the copyright owner. ©Birkh~user Boston, Inc., 1982 Softcover reprint of the hardcover 1st edition 1982

lSBN-13: 978~0-8176-3i06-2

Autres Communications

p.

vi

Preface

p.

vii

Liste des Participants

p.

viii

L. GRUSON & C. PESKINE

variet~s

Courbes de l'espace projectif: de secantes

p.

1

L. GRUSON & C. PESKlNE

Section plane d'une courbe gauche: postulation

p.

33

R. PlENE

Degenerations of complete twisted cubics

p.

37

F. CATANESE

Pluricanonical-Gorenstein-curves

p.

51

W. FULTON & R. LAZARSFELD

Positivity and excess intersection

p.

97

D. LAKSOV

Notes on the evolution of complete correlations

p.

107

Diviseurs speciaux et intersection de cycles dans la Jacobienne d'une courbe algebrique

p.

133

A. HIRSCHOWITZ & M.S. NARASIMHAN

Fibres de 't Hooft speciaux et applications

p.

143

P. LE BARZ

Formules mUlti-secantes pour les courbes gauche quelconques

p.

165

Schubert calculus for complete quadrics

p.

199

Multiple point formulas for maps

p.

237

A. BEAUVILLE

1. VAINSENCHER

S.L. KLEIMAN

AUTRES COMMUNICATIONS FAITES AU COURS DU COLLOQUE E. BALLICO

Postulation formulae for generic elliptic curves.

M. FIORENTINI

Trois theoremes sur les courbes de ~3

F. GAETA

Formes de Cayley-Chow de l'intersection de deux varietes algebriques.

K. HULEK

The normal bundle of a space curve on a quadric.

H. LANGE

Vector bundles on curves and secant planes.

R. LAZARSFELD

varieties with degenerate secant varieties.

G. MARTENS

On the Clifford-index of a curve.

U. PERSSON

Surfaces with maximal Picard numbers.

G. SACCHIERO

Les varietes parametrisant les courbes rationnelles de ~3,