Algebraic Curves and Projective Geometry Proceedings of the Conferen

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1389 E. Ballico

C. Ciliberto

(Eds.)

Algebraic Curves and Projective Geometry Proceedings of the Conference held in Trento, Italy, March 21-25, 1988

Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong

Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann

1389 E. Ballico

C. Ciliberto

(Eds.)

Algebraic Curves and Projective Geometry Proceedings of the Conference held in Trento, Italy, March 21-25, 1988

Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong

Editors

Edoardo Ballico Dipartimento di Matematica, Universita di Trento 38050 Povo (Trento), Italy Ciro Ciliberto Dipartimento di Matematica, Universita di Roma II Via O. Raimondo, 00173 Roma, Italy

Mathematics Subject Classification (1980): 14H99, 14N05, 14N 10, 14J99 ISBN 3-540-51509-7 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51509-7 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 ofthe 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 1989 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper

PREFACE

The conference on "Algebraic curves and projective geometry" was held in Villa Madruzzo, Cognola (Trento) from March 21 to 25, 1988. The meeting has been sponsored and supported by C.I.R.M. (Centro Intemazionale per la Ricerca Matematica, Trento). This volume contains most of the works reported in the formal and informal lectures at the conference. The main topics of the volume are geometry of projective curves and moduli, enumerative and projective geometry, homological algebra and arithmetic surfaces. We liked the idea of inserting at the end of this volume a list of problems and questions; most of them were asked and discussed during the conference. We collected this list mentioning the proposers of the questions and a few related references. We believe that publishing such lists may be a very useful contribution to the mathematical life, and hope this will be done more often. We are very grateful to all participants for their enthusiasm, to the contributors of this volume for their efforts, to the referees for their precious help, and to the CIRM for the organization of the meeting and the assistance in editing this volume.

Edoardo Ballico, University of Trento Ciro Ciliberto, University of Rome

CONTENTS

E. Arrondo, M. Pedreira, I. Sols - On regular and stable ruled surfaces in p3

1

R. Hernandez - Appendix to "On regular and stable ruled surfaces in p3"

16

G. Bolondi, J.C.