Hodge Theory Proceedings of the U.S.-Spain Workshop held in Sant Cug
Over the past 2O years classical Hodge theory has undergone several generalizations of great interest in algebraic geometry. The papers in this volume reflect the recent developments in the areas of: mixed Hodge theory on the cohomology of singular and op
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1246
Hodge Theory Proceedings of the U.S.-Spain Workshop held in Sant Cugat (Barcelona), Spain June 24-30, 1985
Edited by E. Cattani, F. Guillen, A. Kaplan and F. Puerta
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
1246
Hodge Theory Proceedings of the U.S.-Spain Workshop held in Sant Cugat (Barcelona), Spain June 24-30, 1985
Edited by E. Cattani, F. Guillen, A. Kaplan and F. Puerta
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors
Eduardo Cattani Aroldo Kaplan Dep.artmentof Mathematics, University of Massachusetts Amherst, Massachusetts 01003, USA Francisco Guillen Fernando Puerta Departament de Maternatiques ETSEIB Universitat Politecnica de Catalunya Avenida Diagonal 647, 08028 Barcelona, Spain
Mathematics Subject Classification (1980): Primary: 14C30, 32J25 Secondary: 14B05, 14B 15, 14005, 14F40, 14J 15, 32C38, 32G 13, 32G20 ISBN 3-540-17743-4 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-17743-4 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 dats 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 Copyriqht Law.
© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
Introduction This volume contains most of the papers presented at the 1985 U.S.-Spain workshop on Hodge Theory, which took place in June of that year in St.
Cugat del Valles
(Barcelona),
under the
auspices of the Joint Committee for Scientific and Technological Cooperation between the two countries. The methods of harmonic theory introduced by Riemann in the study of algebraic curves and extended by Hodge to higher dimensions, yield important consequences for the structure of smooth
projective
varieties;
prototypical
examples
are
the
decomposition of the complex cohomology groups of such varieties according to Hodge type, and the Lefschetz decomposition in terms of primitive cohomology classes.
Since Hodge,
these ideas have
undergone several generalizations of great interest in algebraic geometry.
This volume focuses on those concerning singular and
open varieties,
families,
and the rational homotopy of varieties,
which have been developed during the past 20 years. The
structure present
in the
local
system of
cohomology
defined by a family of smooth varieties was encoded by Griffiths in the notion of a Some
of
include: Hodge
the
variation of
related
questions
(polarized) explored
in
Hodge
s t ru ct.ur-e l
these
proceedings
.
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