Introduction to Complex Analytic Geometry (Paperback)

Stanislaw Lojasiewicz

ISBN 10: 303487619X / ISBN 13: 9783034876193

Edité par Springer Basel, Basel, 2014

Paperback. 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). The notions of analytic sets and germs are introduced in the second chapter. The main step towards understanding of the local structure of analytic sets is Ruckert's descriptive lemma proved in Chapter III. In the fourth chapter, a study of local structure (normal triples, 1) is followed by an exposition of the basic properties of analytic sets. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. N° de réf. du vendeur 9783034876193

Synopsis :

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).

Détails bibliographiques

Titre : Introduction to Complex Analytic Geometry (...
Éditeur : Springer Basel, Basel
Date d'édition : 2014
Reliure : Paperback
Etat : new