Moduli of curves and Abelian varieties: the Dutch Intercity Seminar on Moduli
Saved in:
| Format: | Book |
|---|---|
| Language: | German |
| Published: |
Braunschweig [u.a.]
Vieweg
1999
|
| Series: | [Aspects of mathematics / E]
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 200 S. |
| ISBN: | 3528031255 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface v
Moduli of Abelian Varieties: A Short Introduction and Survey 1
Gerard van der Geer and Frans Oort
1 Introduction 1
2 Elliptic Curves 2
3 Abelian Varieties 4
4 The Torelli Morphism 9
5 Cycles on the Moduli Space of Abelian Varieties 12
6 The Moduli Space Ag in Positive Characteristic 14
7 The Moduli Space in Mixed Characteristic 17
Remarks on Moduli of Curves 23
Carel Faber and Eduard Looijenga
1 Introduction 23
2 Mapping Class Groups 24
3 The Torelli Group 25
4 Moduli Spaces of Curves 26
5 Deligne Mumford Knudsen Completion 27
6 Covers of Moduli Stacks 28
7 Tautological Classes 29
8 Stability 30
9 A Proarithmetic Hull of the Mapping Class Group 31
10 The Witten Conjecture 32
11 Complete Subvarieties of Moduli Spaces 33
12 Intersection Theory 37
13 Stable Maps and the Virasoro Conjecture 39
A Stratification of a Moduli Space of Polarized Abelian Varieties in
Positive Characteristic 47
Frans Oort
1 Introduction 47
2 Elementary Sequences and Final Filtrations 48
3 Explicit Description of Some of the Strata 52
Contents vii
4 Standard Types 53
5 Moving in a Stratum 54
6 The Raynaud Trick 56
7 Results 59
8 Some Questions 60
Cycles on the Moduli Space of Abelian Varieties 65
Gerard van der Geer
1 Introduction 65
2 The Tautological Subring of Ag 66
3 The Tautological Ring of Ag 70
4 Cycle Relations from Grothendieck Riemann Roch 72
5 On the Torsion of the Class Ap 76
6 The Ekedahl Oort Stratification in Positive Characteristic ... 76
7 The Ekedahl Oort Strata as Degeneracy Loci 78
8 The Degeneracy Locus 1A Fo(p) 82
9 The Cycle Classes of the Strata 83
10 Effectivity of Tautological Classes 87
11 Some Additional Results 88
Locally Symmetric Families of Curves and Jacobians 91
Richard Hain
1 Introduction 91
2 Background and Definitions 94
3 Homomorphisms to Mapping Class Groups 96
4 Maps of Lattices to Mapping Class Groups 97
5 Locally Symmetric Hypersurfaces in Locally Symmetric Varieties 100
6 Geometry of the Jacobian Locus 100
7 Locally Symmetric Families of Curves 103
8 Locally Symmetric Families of Jacobians 104
9 Appendix: An Example 106
A Conjectural Description of the Tautological Ring of the
Moduli Space of Curves 109
Carel Faber
1 Introduction 109
2 Known Results 110
3 The Conjectures and the Evidence 114
4 Calculations 119
5 Other Relations 125
Correspondences between Moduli Spaces of Curves 131
Eduard Looijenga
1 Introduction 131
2 Correspondences for Mapping Class Groups: Closed Surfaces . 133
viii Contents
3 Action of the Correspondences on the Tautological Classes . . 137
4 Hecke Operators Attached to Finite Abelian Covers 139
5 Correspondences via Ramified Covers 141
6 Correspondences Acting on a Lie Algebra 148
Fields, Strings, Matrices and Symmetric Products 151
Robbert Dijkgraaf
1 Introduction 151
2 Particles, Symmetric Products and Fields 155
3 Second quantized Strings 163
4 Light Cone Quantization of Quantum Field Theories 173
5 Light Cone Quantization of String Theories 179
6 Matrix Strings and Interactions 188
7 String Theories in Six Dimensions 194
Addresses 200
|
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| bvnumber | BV012596173 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:30:18Z |
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| series2 | [Aspects of mathematics / E] |
| spelling | Moduli of curves and Abelian varieties the Dutch Intercity Seminar on Moduli Carel Faber ... (eds.) Braunschweig [u.a.] Vieweg 1999 VIII, 200 S. txt rdacontent n rdamedia nc rdacarrier [Aspects of mathematics / E] 33 Courbes algébriques Modules, Théorie des Variétés abéliennes Variëteiten van Abel gtt Abelian varieties Congresses Curves, Algebraic Congresses Moduli theory Congresses Modulraum (DE-588)4183462-8 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Algebraischer Modulraum (DE-588)4141853-0 gnd rswk-swf Modul (DE-588)4129770-2 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)1071861417 Konferenzschrift gnd-content Algebraische Kurve (DE-588)4001165-3 s Modul (DE-588)4129770-2 s DE-604 Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Algebraische Geometrie (DE-588)4001161-6 s Algebraischer Modulraum (DE-588)4141853-0 s Modulraum (DE-588)4183462-8 s Faber, Carel 1962- Sonstige (DE-588)172494168 oth Looijenga, Eduard 1948- Sonstige (DE-588)107785434X oth E] [Aspects of mathematics 33 (DE-604)BV000018737 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008554160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moduli of curves and Abelian varieties the Dutch Intercity Seminar on Moduli Courbes algébriques Modules, Théorie des Variétés abéliennes Variëteiten van Abel gtt Abelian varieties Congresses Curves, Algebraic Congresses Moduli theory Congresses Modulraum (DE-588)4183462-8 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Algebraische Kurve (DE-588)4001165-3 gnd Algebraischer Modulraum (DE-588)4141853-0 gnd Modul (DE-588)4129770-2 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd |
| subject_GND | (DE-588)4183462-8 (DE-588)4001161-6 (DE-588)4001165-3 (DE-588)4141853-0 (DE-588)4129770-2 (DE-588)4140992-9 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Moduli of curves and Abelian varieties the Dutch Intercity Seminar on Moduli |
| title_auth | Moduli of curves and Abelian varieties the Dutch Intercity Seminar on Moduli |
| title_exact_search | Moduli of curves and Abelian varieties the Dutch Intercity Seminar on Moduli |
| title_full | Moduli of curves and Abelian varieties the Dutch Intercity Seminar on Moduli Carel Faber ... (eds.) |
| title_fullStr | Moduli of curves and Abelian varieties the Dutch Intercity Seminar on Moduli Carel Faber ... (eds.) |
| title_full_unstemmed | Moduli of curves and Abelian varieties the Dutch Intercity Seminar on Moduli Carel Faber ... (eds.) |
| title_short | Moduli of curves and Abelian varieties |
| title_sort | moduli of curves and abelian varieties the dutch intercity seminar on moduli |
| title_sub | the Dutch Intercity Seminar on Moduli |
| topic | Courbes algébriques Modules, Théorie des Variétés abéliennes Variëteiten van Abel gtt Abelian varieties Congresses Curves, Algebraic Congresses Moduli theory Congresses Modulraum (DE-588)4183462-8 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Algebraische Kurve (DE-588)4001165-3 gnd Algebraischer Modulraum (DE-588)4141853-0 gnd Modul (DE-588)4129770-2 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd |
| topic_facet | Courbes algébriques Modules, Théorie des Variétés abéliennes Variëteiten van Abel Abelian varieties Congresses Curves, Algebraic Congresses Moduli theory Congresses Modulraum Algebraische Geometrie Algebraische Kurve Algebraischer Modulraum Modul Abelsche Mannigfaltigkeit Aufsatzsammlung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008554160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018737 |
| work_keys_str_mv | AT fabercarel moduliofcurvesandabelianvarietiesthedutchintercityseminaronmoduli AT looijengaeduard moduliofcurvesandabelianvarietiesthedutchintercityseminaronmoduli |