文档介绍：LECTURES PLEX ANALYTIC VARIETIES:
THE LOCAL PARAMETRIZATION THEOREM
BY
R. C. GUNNING
PRINCETON UNIVERSITY PRESS
AND THE
UNIVERSITY OF TOKYO PRESS
PRINCETON, NEW JERSEY
1970
Copyright © 1970, by Princeton University Press
All Rights Reserved
. Card: 73-132628
.: 0-691-08029-1
. 1968: 3244
Published in Japan exclusively
by the University of Tokyo Press;
in other parts of the world by
Princeton University Press
Printed in the United States of America
1.
PREFACE
In introductory courses plex analytic varieties, it
is customary to begin the local description of irreducible sub-
varieties by choosing a system of coordinates in the ambient space
LP such that the subvariety is in a particularly convenient posi-
tion, for example, such that the subvariety appears as a branched
covering space of a coordinate hyperplane zk+l 0
... = zn =
under the natural projection mapping. The existence of such coor-
dinate systems, together with a catalog of the elementary proper-
ties of analytic subvarieties in terms of these coordinate systems,
comprise what may be called the local parametrization theorem for
complex analytic subvarieties. Once this has been established, it
is relatively easy to derive the standard local properties of ana-
lytic subvarieties, and the way is then clear to proceed to more
advanced topics, either on the local or the global level.
These lecture notes treat the local parametrization
theorem, assuming some background knowledge of the general func-
tion theory of plex variables. They contain the mate-
mon to the first parts of several courses of lectures on
complex analytic varieties that I have given in the past few years.
They go further in various directions into the properties -
plex analytic varieties than some recent texts on the subject (such
as L. H$rmander, An Introduction plex Analysis in Several
ii.
Variables; or R. C. Gunning and H. Rossi, Analytic Functions of
plex V