Complex Abelian Varieties and Theta Functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1991
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Abelian varieties are a natural generalization of elliptic curves to higher dimensions, whose geometry and classification are as rich in elegant results as in the one-dimensional ease. The use of theta functions, particularly since Mumford's work, has been an important tool in the study of abelian varieties and invertible sheaves on them. Also, abelian varieties play a significant role in the geometric approach to modern algebraic number theory. In this book, Kempf has focused on the analytic aspects of the geometry of abelian varieties, rather than taking the alternative algebraic or arithmetic points of view. His purpose is to provide an introduction to complex analytic geometry. Thus, he uses Hermitian geometry as much as possible. One distinguishing feature of Kempf's presentation is the systematic use of Mumford's theta group. This allows him to give precise results about the projective ideal of an abelian variety. In its detailed discussion of the cohomology of invertible sheaves, the book incorporates material previously found only in research articles. Also, several examples where abelian varieties arise in various branches of geometry are given as a conclusion of the book |
| Physical Description: | 1 Online-Ressource (IX, 105p) |
| ISBN: | 9783642760792 9783540531685 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-76079-2 |
Staff View
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Record in the Search Index
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9783642760792 9783540531685 |
| issn | 0172-5939 |
| language | English |
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| physical | 1 Online-Ressource (IX, 105p) |
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| publishDate | 1991 |
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| spelling | Kempf, George R. Verfasser aut Complex Abelian Varieties and Theta Functions by George R. Kempf Berlin, Heidelberg Springer Berlin Heidelberg 1991 1 Online-Ressource (IX, 105p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 Abelian varieties are a natural generalization of elliptic curves to higher dimensions, whose geometry and classification are as rich in elegant results as in the one-dimensional ease. The use of theta functions, particularly since Mumford's work, has been an important tool in the study of abelian varieties and invertible sheaves on them. Also, abelian varieties play a significant role in the geometric approach to modern algebraic number theory. In this book, Kempf has focused on the analytic aspects of the geometry of abelian varieties, rather than taking the alternative algebraic or arithmetic points of view. His purpose is to provide an introduction to complex analytic geometry. Thus, he uses Hermitian geometry as much as possible. One distinguishing feature of Kempf's presentation is the systematic use of Mumford's theta group. This allows him to give precise results about the projective ideal of an abelian variety. In its detailed discussion of the cohomology of invertible sheaves, the book incorporates material previously found only in research articles. Also, several examples where abelian varieties arise in various branches of geometry are given as a conclusion of the book Mathematics Geometry, algebraic Global analysis (Mathematics) Algebraic Geometry Analysis Mathematik Thetafunktion (DE-588)4185175-4 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Theta-Reihe (DE-588)4206702-9 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Theta-Reihe (DE-588)4206702-9 s 1\p DE-604 Thetafunktion (DE-588)4185175-4 s 2\p DE-604 https://doi.org/10.1007/978-3-642-76079-2 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 | Kempf, George R. Complex Abelian Varieties and Theta Functions Mathematics Geometry, algebraic Global analysis (Mathematics) Algebraic Geometry Analysis Mathematik Thetafunktion (DE-588)4185175-4 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Theta-Reihe (DE-588)4206702-9 gnd |
| subject_GND | (DE-588)4185175-4 (DE-588)4140992-9 (DE-588)4206702-9 |
| title | Complex Abelian Varieties and Theta Functions |
| title_auth | Complex Abelian Varieties and Theta Functions |
| title_exact_search | Complex Abelian Varieties and Theta Functions |
| title_full | Complex Abelian Varieties and Theta Functions by George R. Kempf |
| title_fullStr | Complex Abelian Varieties and Theta Functions by George R. Kempf |
| title_full_unstemmed | Complex Abelian Varieties and Theta Functions by George R. Kempf |
| title_short | Complex Abelian Varieties and Theta Functions |
| title_sort | complex abelian varieties and theta functions |
| topic | Mathematics Geometry, algebraic Global analysis (Mathematics) Algebraic Geometry Analysis Mathematik Thetafunktion (DE-588)4185175-4 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Theta-Reihe (DE-588)4206702-9 gnd |
| topic_facet | Mathematics Geometry, algebraic Global analysis (Mathematics) Algebraic Geometry Analysis Mathematik Thetafunktion Abelsche Mannigfaltigkeit Theta-Reihe |
| url | https://doi.org/10.1007/978-3-642-76079-2 |
| work_keys_str_mv | AT kempfgeorger complexabelianvarietiesandthetafunctions |