Complex Abelian Varieties:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
|
| Ausgabe: | Second, Augmented Edition |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
302 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-662-06307-1 |
| 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 |
| Umfang: | 1 Online-Ressource (XI, 638 p) |
| ISBN: | 9783662063071 9783642058073 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-06307-1 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423372 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2004 xx o|||| 00||| eng d | ||
| 020 | |a 9783662063071 |c Online |9 978-3-662-06307-1 | ||
| 020 | |a 9783642058073 |c Print |9 978-3-642-05807-3 | ||
| 024 | 7 | |a 10.1007/978-3-662-06307-1 |2 doi | |
| 035 | |a (OCoLC)1165485098 | ||
| 035 | |a (DE-599)BVBBV042423372 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 516.35 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Birkenhake, Christina |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Complex Abelian Varieties |c by Christina Birkenhake, Herbert Lange |
| 250 | |a Second, Augmented Edition | ||
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 2004 | |
| 300 | |a 1 Online-Ressource (XI, 638 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 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 | |
| 650 | 0 | 7 | |a Komplexe Mannigfaltigkeit |0 (DE-588)4031996-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Abelsche Mannigfaltigkeit |0 (DE-588)4140992-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Abelsche Mannigfaltigkeit |0 (DE-588)4140992-9 |D s |
| 689 | 0 | 1 | |a Komplexe Mannigfaltigkeit |0 (DE-588)4031996-9 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Lange, Herbert |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-662-06307-1 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027858789 | |
Datensatz im Suchindex
| DE-BY-TUM_katkey | 2070381 |
|---|---|
| _version_ | 1821931360480133122 |
| 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 |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03412nam a2200565zcb4500</leader><controlfield tag="001">BV042423372</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2004 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783662063071</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-662-06307-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642058073</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-642-05807-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-662-06307-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165485098</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423372</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.35</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Birkenhake, Christina</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Complex Abelian Varieties</subfield><subfield code="c">by Christina Birkenhake, Herbert Lange</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second, Augmented Edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 638 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics</subfield><subfield code="v">302</subfield><subfield code="x">0072-7830</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, algebraic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, partial</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Several Complex Variables and Analytic Spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Komplexe Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4031996-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Abelsche Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4140992-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Abelsche Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4140992-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Komplexe Mannigfaltigkeit</subfield><subfield code="0">(DE-588)4031996-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lange, Herbert</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-662-06307-1</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858789</subfield></datafield></record></collection> |
| id | DE-604.BV042423372 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:48Z |
| institution | BVB |
| isbn | 9783662063071 9783642058073 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858789 |
| oclc_num | 1165485098 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XI, 638 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| 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 |