Algebraic Geometry Sundance 1986 Proceedings of a Conference held at
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
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1311 A. Holme R. Speiser (Eds.)
Algebraic Geometry Sundance 1986 Proceedings of a Conference held at Sundance, Utah, August 12-19, 1986
Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors
Audun Holme Department of Mathematics, University of Bergen Alleqaten 55, 5007 Bergen, Norway Robert Speiser Mathematics Department, Brigham Young University Provo, Utah 84602, USA
Mathematics Subject Classification (1980): 14-06 ISBN 3-540-19236-0 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-19236-0 Springer-Verlag New York Berlin Heidelberg
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1988 Printed in Germany
Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
PREFACE
This book presents some of the proceedings of the conference on Algebraic Geometry held at Sundance, in July 1986, in the mountains near Provo, Utah. Financial support, from the National Science Foundation (grant 86 - 01409) and from Brigham Young University, is gratefully acknowledged. Normally, a proceedings volume collects writups of lecures given at the conference, based on work done earlier, and the present volume, indeed, includes a number of these. We are very pleased, however, that .the bulk of this volume presents research begun or carried out right at Sundance. Some of this new work may not have been done at all, had the conference not brought together the individuals involved. Beautiful surroundings, ample and contiguous spaces for lectures and discussions, meals served right beside the working areas: all contributed to an atmosphere unusually conducive to new work. But the major responsibility for the success of the conference lay, we feel, with the participants. Their enthusiasm, their interests, their eagerness, are reflected in the papers which follow. It is a pleasure to thank them here.
Audun Holme
Robert Speiser
TABLE OF CONTENTS
1
Paolo Alum: The characteristic numbers of smooth plane cubics
9
Susan Jane Colley: Multiple - point formulas and line complexes
23
Steven Diaz and Joe Harris: Geometry of Severi varieties, II: Independence of divisor classes and examples
51
Lawrence Ein, David Eisenbud, and Sheldon Katz: Varieties cut out by quadrics: Scheme - theoretic versus homogeneous generation of ideals
'11
Lawrence Ein: Vanishing theorems for varieties of low codimension
'16
Georges Elencwaig and Patrice Le Barz: Hilb 3P2
101
Brian Harbourne: Iterated blow - ups and moduli for rational surfaces
118
Audun Holme and
