Complex Abelian Varieties:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Ausgabe: | Second, Augmented Edition |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
302 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Abelian varieties are special examples of projective varieties. As such they can be described by a set of homogeneous polynomial equations. The theory of abelian 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. The second edition contains five new chapters which present some of the most important recent result on the subject. Among them are results on automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture |
| Beschreibung: | 1 Online-Ressource (XI, 638 p) |
| ISBN: | 9783662063071 9783642058073 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-06307-1 |
Internformat
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| 245 | 1 | 0 | |a Complex Abelian Varieties |c by Christina Birkenhake, Herbert Lange |
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| 490 | 0 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |v 302 |x 0072-7830 | |
| 500 | |a Abelian varieties are special examples of projective varieties. As such they can be described by a set of homogeneous polynomial equations. The theory of abelian 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. The second edition contains five new chapters which present some of the most important recent result on the subject. Among them are results on automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry, algebraic | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Algebraic Geometry | |
| 650 | 4 | |a Number Theory | |
| 650 | 4 | |a Several Complex Variables and Analytic Spaces | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Birkenhake, Christina |
| author_facet | Birkenhake, Christina |
| author_role | aut |
| author_sort | Birkenhake, Christina |
| author_variant | c b cb |
| building | Verbundindex |
| bvnumber | BV042423372 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165485098 (DE-599)BVBBV042423372 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-06307-1 |
| edition | Second, Augmented Edition |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662063071 9783642058073 |
| issn | 0072-7830 |
| language | English |
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| spelling | Birkenhake, Christina Verfasser aut Complex Abelian Varieties by Christina Birkenhake, Herbert Lange Second, Augmented Edition Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XI, 638 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 they can be described by a set of homogeneous polynomial equations. The theory of abelian 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. The second edition contains five new chapters which present some of the most important recent result on the subject. Among them are results on automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture Mathematics Geometry, algebraic Differential equations, partial Number theory Algebraic Geometry Number Theory Several Complex Variables and Analytic Spaces Mathematik Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Komplexe Mannigfaltigkeit (DE-588)4031996-9 s 1\p DE-604 Lange, Herbert Sonstige oth https://doi.org/10.1007/978-3-662-06307-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Birkenhake, Christina Complex Abelian Varieties Mathematics Geometry, algebraic Differential equations, partial Number theory Algebraic Geometry Number Theory Several Complex Variables and Analytic Spaces Mathematik Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd |
| subject_GND | (DE-588)4031996-9 (DE-588)4140992-9 |
| title | Complex Abelian Varieties |
| title_auth | Complex Abelian Varieties |
| title_exact_search | Complex Abelian Varieties |
| title_full | Complex Abelian Varieties by Christina Birkenhake, Herbert Lange |
| title_fullStr | Complex Abelian Varieties by Christina Birkenhake, Herbert Lange |
| title_full_unstemmed | Complex Abelian Varieties by Christina Birkenhake, Herbert Lange |
| title_short | Complex Abelian Varieties |
| title_sort | complex abelian varieties |
| topic | Mathematics Geometry, algebraic Differential equations, partial Number theory Algebraic Geometry Number Theory Several Complex Variables and Analytic Spaces Mathematik Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd |
| topic_facet | Mathematics Geometry, algebraic Differential equations, partial Number theory Algebraic Geometry Number Theory Several Complex Variables and Analytic Spaces Mathematik Komplexe Mannigfaltigkeit Abelsche Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-3-662-06307-1 |
| work_keys_str_mv | AT birkenhakechristina complexabelianvarieties AT langeherbert complexabelianvarieties |