Value Distribution on Parabolic Spaces
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600 Wilhelm Stoll
Value Distribution on Parabolic Spaces
Springer-Verlag Berlin. Heidelberg • New York 1977
Author Wilhelm Stoll University of Notre Dame Department of Mathematics P.O. Box 398 Notre Dame, Indiana 46556/USA
Library of Congress Cataloging in PnblicaUon Data
St ell, Wilhelm. Value distribution on parabolic spaces. (Lecture notes in mathematics : 600) Bibliography: p. Includes index. 1. A m a l ~ i c mappings. 2 . Value distribution theory. 3- Pseudoconvex domains. I. Title. II. Title: Parabolic spaces. III. Series: Lecture notes in mathematics IBerlin) ; 600. QA331. S86 53-5'.73 77-987~
A M S Subject Classifications (1970): 32 F15, 32 H 25, 32 H 99 ISBN 3-540-08341-3 ISBN 0-387-08341-3
Springer-Verlag Berlin • Heidelberg • N e w York Springer-Verlag N e w York • Heidelberg • Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin • Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
PREFACE
A land mark in value distribution theory of holomorphic maps is
the paper
[33] of Griffiths and King extending Carlson and Griffiths
[8]. Outstanding new results are obtained.
A defect relation for
holomorphic maps of affine algebraic varieties into projective algebraic varieties is established.
However,
stood.
[33] is not easily under-
During the Spring of 1974, I lectured to my students on the topic
of [33] to explain and to clarify the theory.
Notes
[82] were written
in the Spring of 1975. This is an abbreviated and condensed version
of [82]. The theory has been extended to parabolic elementary properties
are studied.
as for instance the Ricci function, dominator,
relation.
spaces whose
New results and new concepts appear, the Jacobian sections and the
which are fundamental to the derivation of the defect
In devising this structure I tried to bring out the internal
beauty of the subject matter and to exhibit the close connections to the earlier theory in [2],
of
[89] and [67].
I strived to be clear and precise in the proofs.
Tung [87] helped immensely.
a list of general assumptions Hopefully,
To facilitate matters
The results
a detailed index,
and references have been provided.
these notes will help to clarify the subject matter and
provide new insights.
I wish to thank Madelyn King for typing this manuscript.
The
research was partially supported by the National Science Foundation successively under the Grants NSF GP 20139 and MPS 75-07086.
Wilhelm Stoll University of Notre Dame
For those who want to have more details and more supporting
material,
[82]
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