Introduction
The study of singularities of analytic functions can be considered
area of the theory of functions of several complex variables and
braic/analytic geometry. It has in the meantime, together with th
of singularities of differentiable mappings, developed into an ind
subject, singularity theory. Through its connections with very ma
mathematical areas and applications to natural and economic scie
in technology (for example, under the heading 'catastrophe theo
theory has aroused great interest. The particular appeal, but also
ticular difficulty, lies in the fact that deep results and methods from
branches of mathematics come into play here.
The aim of this book is to present the foundations of the theory
tions of several complex variables and on this basis to develop the fu
tal concepts of the theory of isolated singularities of holomorphic
systematically. It is derived from lectures given by the author to
matics students in their third and fourth year to introduce them to
research questions in the area of the theory of functions of several v
The book has its genesis in this. As prerequisites we assume only
ductory knowledge of the theory of functions of a single complex
and of algebra, such as students will normally acquire in their first t
of study. The first two chapters correspond to a continuation of th
on complex analysis and deal with Riemann surfaces and the theory
tions of several complex variables. They also present an introduction
complex geometry. In the third chapter the results will be applied
mation and classification of isolated singularities of holomorphic f
These three chapters have grown from notes for the author's lec
Riemann surfaces and the theory of functions of several complex
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