Singularities and Topology of Hypersurfaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1992
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | From the very beginning, algebraic topology has developed under the influence of the problems posed by trying to understand the topological properties of complex algebraic varieties (e.g., the pioneering work by Poincare and Lefschetz). Especially in the work of Lefschetz [Lf2], the idea is made explicit that singularities are important in the study of the topology even in the case of smooth varieties. What is known nowadays about the topology of smooth and singular varieties is quite impressive. The many existing results may be roughly divided into two classes as follows: (i) very general results or theories, like stratified Morse theory and (mixed) Hodge theory, see, for instance, Goresky-MacPherson [GM], Deligne [Del], and Steenbrink [S6]; and (ii) specific topics of great subtlety and beauty, like the study of the funda mental group of the complement in [p>2 of a singular plane curve initiated by Zariski or Griffiths' theory relating the rational differential forms to the Hodge filtration on the middle cohomology group of a smooth projective hypersurface. The aim of this book is precisely to introduce the reader to some topics in this latter class. Most of the results to be discussed, as well as the related notions, are at least two decades old, and specialists use them intensively and freely in their work. Nevertheless, it is impossible to find an adequate introduction to this subject, which gives a good feeling for its relations with other parts of algebraic geometry and topology |
| Beschreibung: | 1 Online-Ressource (XVI, 263p. 44 illus) |
| ISBN: | 9781461244042 9780387977096 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4612-4404-2 |
Internformat
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Datensatz im Suchindex
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| author | Dimca, Alexandru |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4404-2 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461244042 9780387977096 |
| issn | 0172-5939 |
| language | English |
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| spelling | Dimca, Alexandru Verfasser aut Singularities and Topology of Hypersurfaces by Alexandru Dimca New York, NY Springer New York 1992 1 Online-Ressource (XVI, 263p. 44 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 From the very beginning, algebraic topology has developed under the influence of the problems posed by trying to understand the topological properties of complex algebraic varieties (e.g., the pioneering work by Poincare and Lefschetz). Especially in the work of Lefschetz [Lf2], the idea is made explicit that singularities are important in the study of the topology even in the case of smooth varieties. What is known nowadays about the topology of smooth and singular varieties is quite impressive. The many existing results may be roughly divided into two classes as follows: (i) very general results or theories, like stratified Morse theory and (mixed) Hodge theory, see, for instance, Goresky-MacPherson [GM], Deligne [Del], and Steenbrink [S6]; and (ii) specific topics of great subtlety and beauty, like the study of the funda mental group of the complement in [p>2 of a singular plane curve initiated by Zariski or Griffiths' theory relating the rational differential forms to the Hodge filtration on the middle cohomology group of a smooth projective hypersurface. The aim of this book is precisely to introduce the reader to some topics in this latter class. Most of the results to be discussed, as well as the related notions, are at least two decades old, and specialists use them intensively and freely in their work. Nevertheless, it is impossible to find an adequate introduction to this subject, which gives a good feeling for its relations with other parts of algebraic geometry and topology Mathematics Geometry, algebraic Algebraic topology Algebraic Geometry Algebraic Topology Mathematik Hyperfläche (DE-588)4161054-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Hyperflächensingularität (DE-588)4161055-6 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Hyperfläche (DE-588)4161054-4 s Singularität Mathematik (DE-588)4077459-4 s Algebraische Topologie (DE-588)4120861-4 s 1\p DE-604 Hyperflächensingularität (DE-588)4161055-6 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-4404-2 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 | Dimca, Alexandru Singularities and Topology of Hypersurfaces Mathematics Geometry, algebraic Algebraic topology Algebraic Geometry Algebraic Topology Mathematik Hyperfläche (DE-588)4161054-4 gnd Algebraische Topologie (DE-588)4120861-4 gnd Hyperflächensingularität (DE-588)4161055-6 gnd Singularität Mathematik (DE-588)4077459-4 gnd |
| subject_GND | (DE-588)4161054-4 (DE-588)4120861-4 (DE-588)4161055-6 (DE-588)4077459-4 |
| title | Singularities and Topology of Hypersurfaces |
| title_auth | Singularities and Topology of Hypersurfaces |
| title_exact_search | Singularities and Topology of Hypersurfaces |
| title_full | Singularities and Topology of Hypersurfaces by Alexandru Dimca |
| title_fullStr | Singularities and Topology of Hypersurfaces by Alexandru Dimca |
| title_full_unstemmed | Singularities and Topology of Hypersurfaces by Alexandru Dimca |
| title_short | Singularities and Topology of Hypersurfaces |
| title_sort | singularities and topology of hypersurfaces |
| topic | Mathematics Geometry, algebraic Algebraic topology Algebraic Geometry Algebraic Topology Mathematik Hyperfläche (DE-588)4161054-4 gnd Algebraische Topologie (DE-588)4120861-4 gnd Hyperflächensingularität (DE-588)4161055-6 gnd Singularität Mathematik (DE-588)4077459-4 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebraic topology Algebraic Geometry Algebraic Topology Mathematik Hyperfläche Algebraische Topologie Hyperflächensingularität Singularität Mathematik |
| url | https://doi.org/10.1007/978-1-4612-4404-2 |
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