Complex Abelian Varieties:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1992
|
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
302 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi. The subject of this book is the theory of abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results onJacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics, to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions |
| Physical Description: | 1 Online-Ressource (VIII, 435 p) |
| ISBN: | 9783662027882 9783662027905 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-02788-2 |
Staff View
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| 500 | |a Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi. The subject of this book is the theory of abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results onJacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics, to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions | ||
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662027882 9783662027905 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858631 |
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| physical | 1 Online-Ressource (VIII, 435 p) |
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| publishDate | 1992 |
| publishDateSearch | 1992 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Lange, Herbert Verfasser aut Complex Abelian Varieties by Herbert Lange, Christina Birkenhake Berlin, Heidelberg Springer Berlin Heidelberg 1992 1 Online-Ressource (VIII, 435 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 302 0072-7830 Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian varieties originated in the beginning of the ninetheenth centrury with the work of Abel and Jacobi. The subject of this book is the theory of abelian varieties over the field of complex numbers, and it covers the main results of the theory, both classic and recent, in modern language. It is intended to give a comprehensive introduction to the field, but also to serve as a reference. The focal topics are the projective embeddings of an abelian variety, their equations and geometric properties. Moreover several moduli spaces of abelian varieties with additional structure are constructed. Some special results onJacobians and Prym varieties allow applications to the theory of algebraic curves. The main tools for the proofs are the theta group of a line bundle, introduced by Mumford, and the characteristics, to be associated to any nondegenerate line bundle. They are a direct generalization of the classical notion of characteristics of theta functions Mathematics Geometry, algebraic Number theory Algebraic Geometry Number Theory Mathematik Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Komplexe Mannigfaltigkeit (DE-588)4031996-9 s 1\p DE-604 Birkenhake, Christina Sonstige oth https://doi.org/10.1007/978-3-662-02788-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lange, Herbert Complex Abelian Varieties Mathematics Geometry, algebraic Number theory Algebraic Geometry Number Theory Mathematik Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| subject_GND | (DE-588)4140992-9 (DE-588)4031996-9 |
| title | Complex Abelian Varieties |
| title_auth | Complex Abelian Varieties |
| title_exact_search | Complex Abelian Varieties |
| title_full | Complex Abelian Varieties by Herbert Lange, Christina Birkenhake |
| title_fullStr | Complex Abelian Varieties by Herbert Lange, Christina Birkenhake |
| title_full_unstemmed | Complex Abelian Varieties by Herbert Lange, Christina Birkenhake |
| title_short | Complex Abelian Varieties |
| title_sort | complex abelian varieties |
| topic | Mathematics Geometry, algebraic Number theory Algebraic Geometry Number Theory Mathematik Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd |
| topic_facet | Mathematics Geometry, algebraic Number theory Algebraic Geometry Number Theory Mathematik Abelsche Mannigfaltigkeit Komplexe Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-3-662-02788-2 |
| work_keys_str_mv | AT langeherbert complexabelianvarieties AT birkenhakechristina complexabelianvarieties |