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Field name	Details
Dewey Class	515
Title	Introduction to Complex Analytic Geometry ([EBook] /) / by Stanisław Łojasiewicz.
Author	Łojasiewicz, Stanisław
Other name(s)	SpringerLink (Online service)
Publication	Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 1991.
Physical Details	XIV, 523 p. : online resource.
ISBN	9783034876179
Summary Note	facts. An elementary acquaintance with topology, algebra, and analysis (in cluding the notion of a manifold) is sufficient as far as the understanding of this book is concerned. All the necessary properties and theorems have been gathered in the preliminary chapters -either with proofs or with references to standard and elementary textbooks. The first chapter of the book is devoted to a study of the rings Oa of holomorphic functions. The notions of analytic sets and germs are introduced in the second chapter. Its aim is to present elementary properties of these objects, also in connection with ideals of the rings Oa. The case of principal germs (§5) and one-dimensional germs (Puiseux theorem, §6) are treated separately. The main step towards understanding of the local structure of analytic sets is Ruckert's descriptive lemma proved in Chapter III. Among its conse quences is the important Hilbert Nullstellensatz (§4). In the fourth chapter, a study of local structure (normal triples, § 1) is followed by an exposition of the basic properties of analytic sets. The latter includes theorems on the set of singular points, irreducibility, and decom position into irreducible branches (§2). The role played by the ring 0 A of an analytic germ is shown (§4). Then, the Remmert-Stein theorem on re movable singularities is proved (§6). The last part of the chapter deals with analytically constructible sets (§7).:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-7617-9
Links to Related Works	Subject References: Algebraic Geometry . Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Łojasiewicz, Stanisław . Corporate Authors: SpringerLink (Online service) . Classification: 515 .

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Introduction to Complex Analytic Geometry

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