Enumerative Geometry Proceedings of a Conference held in Sitges, Spa

The central topics of this volume are enumerative geometry and intersection theory. The contributions are original (refereed) research papers.

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1436 S. Xamb6-Descamps (Ed.)

Enumerative Geometry Proceedings of a Conference held in Sitges, Spain, June 1-6, 1987

Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona

Editor

Sebastian Xamb6-Descamps Departamento Algebra Facultad de Matematicas Universidad Complutense 28040 Madrid, Spain

Mathematics Subject Classification (1980): 14N10, 14N05, 14Cxx ISBN 3-540-52811-3 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-52811-3 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 ofthis 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 1990 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper

PREFACE

Ten of the eleven papers collected in this volume correlate closely with the contents of corresponding lectures presented at the conference on Enumerative Geometry held in Sitges during the first week of June 1987. The paper that does not was included because it fits well with the subjects dealt with in that week. Written accounts of the lectures that did not evolve into a contribution to this volume are being published elsewhere. The Conference was organized by the "Departament d'Algebra i Geometria" of the "Universitat de Barcelona". E. Casas Alvero (Univ. of Barcelona) and the editor of this volume acted as Organizing Committee and, together with P. Le Barz (Univ. of Nice), as Scientific Committee. The sponsors of the Conference were CAICYT (Comision Asesora de Investigacion Cientifica y Tecnologica, through project 326­84); the University of Barcelona; CIRIT (Comrnissio Interdepartamental de Recerca i Innovaci6 Tecnologica}; and DGU (Direcci6 General d'Universitats); all their support is gratefully acknowledged here. Our gratitude also to the town of Sitges, and in particular to the City Hall (Ajuntament), for the facilities they put at our disposal; to the graduate students that helped in a variety of tasks; and to Imma, the Secretary of the Department of Algebra and Geometry of the University of Barcelona, whose charm and savvy were invaluable. It is a pleasure, and a duty, to thank the contributors to this volume for their endeavors; the referees for their patience and generosity; the speakers at the conference; and all the participants. For ultimately the success of a conference rests on all of them working coherently together in the task of producing and sharing new ideas and knowledge.

Finally I would like to thank Steven L. Kleiman for the enlightening discussions no