Introduction to Complex Analytic Geometry

Stanislaw Lojasiewicz (Autor)

Buch | Hardcover

XIV, 523 Seiten

1991
Springer Basel (Verlag)
978-3-7643-1935-9 (ISBN)

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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).

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.

Erscheint lt. Verlag	1.1.1991
Zusatzinfo	XIV, 523 p.
Verlagsort	Basel
Sprache	englisch
Gewicht	1210 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • Algebraic Geometry • Algebraische Geometrie • Analysis • Boundary element method • Complex Analysis • Equation • Factor • Finite • Geometry • Hardcover, Softcover / Mathematik/Analysis • HC/Mathematik/Analysis • holomorphic function • Microsoft Access • Proof • Theorem • Time • Tool • Topology
ISBN-10	3-7643-1935-6 / 3764319356
ISBN-13	978-3-7643-1935-9 / 9783764319359
Zustand	Neuware