Introduction to Complex Analytic Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1991
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | facts. An elementary acquaintance with topology, algebra, and analysis (including 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 consequences 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 decomposition into irreducible branches (§2). The role played by the ring O A of an analytic germ is shown (§4). Then, the Remmert-Stein theorem on removable singularities is proved (§6). The last part of the chapter deals with analytically constructible sets (§7) |
| Beschreibung: | 1 Online-Ressource (XIV, 523 p) |
| ISBN: | 9783034876179 9783034876193 |
| DOI: | 10.1007/978-3-0348-7617-9 |
Internformat
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| 500 | |a facts. An elementary acquaintance with topology, algebra, and analysis (including 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 consequences 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 decomposition into irreducible branches (§2). The role played by the ring O A of an analytic germ is shown (§4). Then, the Remmert-Stein theorem on removable singularities is proved (§6). The last part of the chapter deals with analytically constructible sets (§7) | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Łojasiewicz, Stanisław |
| author_facet | Łojasiewicz, Stanisław |
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| author_sort | Łojasiewicz, Stanisław |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7617-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034876179 9783034876193 |
| language | English |
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| spelling | Łojasiewicz, Stanisław Verfasser aut Introduction to Complex Analytic Geometry by Stanisław Łojasiewicz Basel Birkhäuser Basel 1991 1 Online-Ressource (XIV, 523 p) txt rdacontent c rdamedia cr rdacarrier facts. An elementary acquaintance with topology, algebra, and analysis (including 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 consequences 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 decomposition into irreducible branches (§2). The role played by the ring O A of an analytic germ is shown (§4). Then, the Remmert-Stein theorem on removable singularities is proved (§6). The last part of the chapter deals with analytically constructible sets (§7) Mathematics Geometry, algebraic Global analysis (Mathematics) Analysis Algebraic Geometry Mathematik Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Komplexe analytische Geometrie (DE-588)4280577-6 gnd rswk-swf Komplexe analytische Geometrie (DE-588)4280577-6 s 1\p DE-604 Analytische Geometrie (DE-588)4001867-2 s 2\p DE-604 https://doi.org/10.1007/978-3-0348-7617-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Łojasiewicz, Stanisław Introduction to Complex Analytic Geometry Mathematics Geometry, algebraic Global analysis (Mathematics) Analysis Algebraic Geometry Mathematik Analytische Geometrie (DE-588)4001867-2 gnd Komplexe analytische Geometrie (DE-588)4280577-6 gnd |
| subject_GND | (DE-588)4001867-2 (DE-588)4280577-6 |
| title | Introduction to Complex Analytic Geometry |
| title_auth | Introduction to Complex Analytic Geometry |
| title_exact_search | Introduction to Complex Analytic Geometry |
| title_full | Introduction to Complex Analytic Geometry by Stanisław Łojasiewicz |
| title_fullStr | Introduction to Complex Analytic Geometry by Stanisław Łojasiewicz |
| title_full_unstemmed | Introduction to Complex Analytic Geometry by Stanisław Łojasiewicz |
| title_short | Introduction to Complex Analytic Geometry |
| title_sort | introduction to complex analytic geometry |
| topic | Mathematics Geometry, algebraic Global analysis (Mathematics) Analysis Algebraic Geometry Mathematik Analytische Geometrie (DE-588)4001867-2 gnd Komplexe analytische Geometrie (DE-588)4280577-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Global analysis (Mathematics) Analysis Algebraic Geometry Mathematik Analytische Geometrie Komplexe analytische Geometrie |
| url | https://doi.org/10.1007/978-3-0348-7617-9 |
| work_keys_str_mv | AT łojasiewiczstanisław introductiontocomplexanalyticgeometry |