Toroidal Groups Line Bundles, Cohomology and Quasi-Abelian Varieties
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Yukitaka Abe Klaus Kopfermann
Toroidal Groups Line Bundles, Cohomology and Quasi-Abelian Varieties
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Authors Yukitaka Abe Department of Mathematics Faculty of Science Toyama University Gofuku 3190 Toyama 930-8555, Japan E-mail: [email protected] Klaus Kopfermann Institut für Mathematik Universität Hannover Welfengarten 1 30167 Hannover, Germany E-mail: [email protected]
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Mathematics Subject Classification (2000): 22E10, 22E99 ISSN 0075-8434 ISBN 3-540-41989-6 Springer-Verlag Berlin Heidelberg New York 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 any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2001 Printed in Germany Typesetting: Camera-ready TEX output by the authors SPIN: 10836500 41/3142-543210 - Printed on acid-free paper
Preface
Toroidal groups
are
the missing links between torus groups and any
complex Lie
pseudoconvexity and groups. Many phenomena understood be the structure of cohomology groups can only through the concept of toroidal groups. The different behavior of the cohomology groups of complex of
Lie groups
pearing
can
complex Lie
be characterized
groups such
as
by the properties of their toroidal
groups ap-
in their centers.
Toroidal groups have not been treated systematically in a book. So the oldest living mathematician who worked in this field and the youngest working in it decided to
give
a
comprehensive survey problems.
about the main results concerning these
groups and to discuss open
Toroidal groups
are
the non-compact
generalization of
the torus groups. As
complex manifolds they are convex in the sense of Andreotti and Grauert. As complex Lie groups some of them have a similar behavior to complex tori, others whence comare different with for example non-Hausdorff cohomology groups, pletely
new
methods must be used.
properties of
The aim of these lecture notes is to describe the fundamental
toroidal groups. As
a
result of the
of
meromorphic
This
theory
Conference
-
"
in honour of SOPHus LIE 100 Years after
reduction theorem the
interest. Their basic
are special chapter with the Main Theorem.
Abelian varieties
Sophus
-
was
Lie" in
introduced to
Leipzig,
on
a
Hannover and
wide
July 8-9,
The first-named author wishes to thank the ALEXANDER F
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