Introduction to complex analytic geometry
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. Though many of the results presented are relatively modern, they are already part of the classical tool-kit of workers in analytic and algebraic geometry and in analysis, for example: the theorems of Chevalley on constructible sets, of Remmert-Stein on removable singularities, of Andreotti-Stoll on the fib…
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- Full title :Introduction to complex analytic geometry / Stanisław Łojasiewicz ; translated from the Polish by Maciej Klimek.
Summary
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. Though many of the results presented are relatively modern, they are already part of the classical tool-kit of workers in analytic and algebraic geometry and in analysis, for example: the theorems of Chevalley on constructible sets, of Remmert-Stein on removable singularities, of Andreotti-Stoll on the fibres of a finite mapping, and of Andreotti-Salmon on factoriality of the Grassmannian. The chapter on the relationship between analytic and algebraic geometry is particularly illuminating. This book should be regarded as an introduction. Its aim is to familiarize the reader with a basic range of problems, using means as elementary as possible. At the same time, the author's intention is to give the reader accesss to complete proofs without the need to rely on so-called 'well-known' facts. All the necessary properties and theorems have been gathered in the first chapters - either with proofs or with references to standard and elementary textbooks.
Read More ↓Edition Statements
- Publication Date:1991.
Publication Statements
- Publisher(s):Birkhäuser Verlag
- Place of Publication:Basel
- Language:eng
- Publication Date:1991.
The Physical Object
- Description:1 online resource (xiv, 523 pages) : : illustrations
Edition Identifiers
- ISBN:9783034876179, 3034876173
- DOI:10.1007/978-3-0348-7617-9
- oclc:ocn680563805
- LC Classification:QA331.7
- Dewey Decimal:515/.9
Table of Contents
A. Algebra -- B. Topology -- C. Complex analysis -- I. Rings of germs of holomorphic functions -- II. Analytic sets, analytic germs and their ideals -- III. Fundamental lemmas -- IV. Geometry of analytic sets -- V. Holomorphic mappings -- VI. Normalization -- VII. Analyticity and algebraicity -- References -- Notation index.
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