Introduction To Complex Analytic Geometry Stanislaw Lojasiewicz by Stanislaw Lojasiewicz 9783034876193, 303487619X instant download after payment.

The subject of this book is analytic geometry understood as the geometry of analytic sets (or, more generally, analytic spaces), i.e., sets described locally by systems of analytic equations C). Except for the last chapter, mostly local problems are investigated and, throughout the book, only the complex case is studied. From the purely geometric point of view, the real case is more natural and more general. But it displays fewer regularities and - by and large - the corresponding theory is more difficult. The complex structure is richer. Hence one can expect deeper results. Indeed, some phenomena, such as analyticity of the set of singular points (see IV. 24) or analyticity of proper images (Remmert's theorem, see V. 5.1), do not have counterparts in the real case. More than anything else, the beauty of the interplay between the geometric and algebraic phenomena constitutes the main attraction of the "complex" theory.
This book should be regarded as an introduction. It does not pretend to reflect the entire theory. Its aim is to familiarize the reader with the basic range of problems, using means as elementary as possible. They belong to
complex analysis, commutative algebra, and set topology (the methods of algebraic topology have not been employed), and are gathered in the first three preliminary chapters.