Complex Analysis Proceedings of the Summer School Held at the Intern
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950 Complex Analysis Proceedings of the Summer School Held at the International Centre forTheoretical Physics Trieste July 5-30, 1980
Edited by J. Eells
Springer-Verlag Berlin Heidelberg New York 1982
Editor James Eells University of Warwick, Mathematics Institute Coventry CV4 7AL, England
AMS Subject Classifications (1980): 32-XX, 53-XX, 58-XX ISBN 3-540-11596-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-11596-X Springer-Verlag New 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 "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1982 Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
FOREWORD A summer seminar in complex analysis took place in Trieste (Italy) during July 1980 at the International Centre for Theoretical Physics of the International Atomic Energy Agency (Vienna, Austria) and t h e United Nations Educational, Scientific and Cultural Organization (Paris, France), on the invitation of its Director, Professor Abdus Salam.
The
course was organised by the late Professor Aldo Andreotti and myself. The main lectures included the following: M. G. Eastwood
Twi s t or Theory (The Penrose Transform)
L. Lemaire and J. C. Wood
Introduct ion to Analysis on Complex Manifolds
M. Nacinov ic h
Complex Analysis and complexes of Differential Operators
M. S. Narasimhan
Deformations of Complex Structures and Holomorphic Vector Bund les
w.
Introduction to Value Di stribution Theory of Meromorphic Map s
Stoll
D. Sundararaman
Compact Hausdorff Transversally Holomorphic Foliations
G. Trautman
Holomorphic Vector Bundles and Yang Mills Fields
In addition to these main l ecture courses the re were mini-courses (3 to 6 lectures), as well as research lectures.
The prese nt volume is
a collection of revised versions o f some of t hese.
They are largely
self-contained; however, an accessible refere nce during the summer was Complex Analysis and Its Applicat i ons, edited by A. Andreotti, J . Eell s , and F. Gherardelli, ICTP (197 6 , Volumes 1- 3). I would like to thank all the lecturers (named and unnamed) for t heir efforts during the course.
I know that in turn they join me in
expressing our appreciation of the truly exceptional admin i strative and secretarial staff of the Centre .
James Ee lls
CONTENTS
M. G. EASTWOOD Twister Theory (The Penrose Transform) .........•.•....•..•.• 1 L. LEMAIRE and J. C. WOOD An Introduction to Analysis on Complex Manifolds .......•... 12 M. NACINOVICH Complex Analysis and Complexes of Differential Operators
105
M. S. NARASIMHAN Deformations of Complex Structures and Holomorphic Vector Bundles .... ..•.••...........................••.•.....
