Topological Methods in Algebraic Geometry: Reprint of the 1978 Edition
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1995
|
| Schriftenreihe: | Classics in Mathematics
131 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954 |
| Beschreibung: | 1 Online-Ressource (XI, 234p) |
| ISBN: | 9783642620188 9783540586630 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-642-62018-8 |
Internformat
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Datensatz im Suchindex
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| author | Hirzebruch, Friedrich |
| author_facet | Hirzebruch, Friedrich |
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| author_variant | f h fh |
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| bvnumber | BV042422845 |
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| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-62018-8 |
| format | Electronic eBook |
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| issn | 0072-7830 |
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| spelling | Hirzebruch, Friedrich Verfasser aut Topological Methods in Algebraic Geometry Reprint of the 1978 Edition by Friedrich Hirzebruch Berlin, Heidelberg Springer Berlin Heidelberg 1995 1 Online-Ressource (XI, 234p) txt rdacontent c rdamedia cr rdacarrier Classics in Mathematics 131 0072-7830 In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954 Mathematics Geometry, algebraic Algebraic topology Algebraic Topology Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Topologische Methode (DE-588)4312758-7 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Algebraische Geometrie (DE-588)4001161-6 s Topologie (DE-588)4060425-1 s 2\p DE-604 Topologische Methode (DE-588)4312758-7 s 3\p DE-604 https://doi.org/10.1007/978-3-642-62018-8 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hirzebruch, Friedrich Topological Methods in Algebraic Geometry Reprint of the 1978 Edition Mathematics Geometry, algebraic Algebraic topology Algebraic Topology Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd Topologie (DE-588)4060425-1 gnd Topologische Methode (DE-588)4312758-7 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4060425-1 (DE-588)4312758-7 (DE-588)4113937-9 |
| title | Topological Methods in Algebraic Geometry Reprint of the 1978 Edition |
| title_auth | Topological Methods in Algebraic Geometry Reprint of the 1978 Edition |
| title_exact_search | Topological Methods in Algebraic Geometry Reprint of the 1978 Edition |
| title_full | Topological Methods in Algebraic Geometry Reprint of the 1978 Edition by Friedrich Hirzebruch |
| title_fullStr | Topological Methods in Algebraic Geometry Reprint of the 1978 Edition by Friedrich Hirzebruch |
| title_full_unstemmed | Topological Methods in Algebraic Geometry Reprint of the 1978 Edition by Friedrich Hirzebruch |
| title_short | Topological Methods in Algebraic Geometry |
| title_sort | topological methods in algebraic geometry reprint of the 1978 edition |
| title_sub | Reprint of the 1978 Edition |
| topic | Mathematics Geometry, algebraic Algebraic topology Algebraic Topology Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd Topologie (DE-588)4060425-1 gnd Topologische Methode (DE-588)4312758-7 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebraic topology Algebraic Topology Algebraic Geometry Mathematik Algebraische Geometrie Topologie Topologische Methode Hochschulschrift |
| url | https://doi.org/10.1007/978-3-642-62018-8 |
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