The geometry of moduli spaces of sheaves: a publication of the Max-Planck-Institut für Mathematik, Bonn
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Braunschweig [u.a.]
Vieweg
1997
|
| Schriftenreihe: | [Aspects of mathematics / E]
31 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 269 S. |
| ISBN: | 3528069074 |
Internformat
MARC
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| 245 | 1 | 0 | |a The geometry of moduli spaces of sheaves |b a publication of the Max-Planck-Institut für Mathematik, Bonn |c Daniel Huybrechts ; Manfred Lehn |
| 264 | 1 | |a Braunschweig [u.a.] |b Vieweg |c 1997 | |
| 300 | |a XIV, 269 S. | ||
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Datensatz im Suchindex
| _version_ | 1804125743033090048 |
|---|---|
| adam_text | Contents
Introduction x
I General Theory 1
1 Preliminaries 3
1.1 Some Homological Algebra 3
1.2 Semistable Sheaves 9
1.3 The Harder Narasimhan Filtration 14
1.4 An Example 19
1.5 Jordan Holder Filtration and S Equivalence 22
1.6 ^ Semistability 24
1.7 Boundedness I 27
2 Families of Sheaves 32
2.1 Flat Families and Determinants 32
2.2 Grothendieck s Quot Scheme 38
2.3 The Relative Harder Narasimhan Filtration 45
Appendix
2.A Flag Schemes and Deformation Theory 48
2.B AResultofLangton 55
3 The Grauert Miilich Theorem 57
3.1 Statement and Proof 58
3.2 Finite Coverings and Tensor Products 62
3.3 Boundedness II 68
3.4 The Bogomolov Inequality 71
Appendix
3.A e Stability and Some Estimates 74
4 Moduli Spaces 79
4.1 The Moduli Functor 80
4.2 Group Actions 81
4.3 The Construction — Results 88
4.4 The Construction — Proofs 93
4.5 Local Properties and Dimension Estimates 101
4.6 Universal Families 105
Appendix
4.A Gieseker s Construction 109
4.B Decorated Sheaves 110
4.C Change of Polarization 114
II Sheaves on Surfaces 119
5 Construction Methods 121
5.1 The Serre Correspondence 123
5.2 Elementary Transformations 129
5.3 Examples of Moduli Spaces 131
6 Moduli Spaces on K3 Surfaces 141
6.1 Low Dimensional 141
6.2 ... and Higher Dimensional Moduli Spaces 150
Appendix
6. A The Irreducibility of the Quot scheme 157
7 Restriction of Sheaves to Curves 160
7.1 Flenner s Theorem 160
7.2 The Theorems of Mehta and Ramanathan 164
7.3 Bogomolov s Theorems 170
8 Line Bundles on the Moduli Space 178
8.1 Construction of Determinant Line Bundles 178
8.2 A Moduli Space for /x Semistable Sheaves 185
8.3 The Canonical Class of the Moduli Space 195
9 Irreducibility and Smoothness 199
9.1 Preparations 199
9.2 The Boundary 201
9.3 Generic Smoothness 202
9.4 Irreducibility 203
9.5 Proof of Theorem 9.2.2 204
9.6 Proof of Theorem 9.3.2 210
10 Symplectic Structures 215
10.1 Trace Map, Atiy ah Class and Kodaira Spencer Map 215
10.2 The Tangent Bundle 222
10.3 Forms on the Moduli Space 223
10.4 Non Degeneracy of Two Forms 226
11 Birational properties 230
11.1 Kodaira Dimension of Moduli Spaces 230
11.2 More Results 235
11.3 Examples 238
Bibliography 244
Index 261
Glossary of Notations 265
|
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| dewey-ones | 514 - Topology |
| dewey-raw | 514.224 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011241443 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:06:24Z |
| institution | BVB |
| isbn | 3528069074 |
| language | German |
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| physical | XIV, 269 S. |
| publishDate | 1997 |
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| publisher | Vieweg |
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| series2 | [Aspects of mathematics / E] |
| spelling | Huybrechts, Daniel 1966- Verfasser (DE-588)113483716 aut The geometry of moduli spaces of sheaves a publication of the Max-Planck-Institut für Mathematik, Bonn Daniel Huybrechts ; Manfred Lehn Braunschweig [u.a.] Vieweg 1997 XIV, 269 S. txt rdacontent n rdamedia nc rdacarrier [Aspects of mathematics / E] 31 Garbe Mathematik (DE-588)4019261-1 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Garbe Mathematik (DE-588)4019261-1 s Algebraische Geometrie (DE-588)4001161-6 s Modulraum (DE-588)4183462-8 s 1\p DE-604 Lehn, Manfred Verfasser aut E] [Aspects of mathematics 31 (DE-604)BV000018737 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007545028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Huybrechts, Daniel 1966- Lehn, Manfred The geometry of moduli spaces of sheaves a publication of the Max-Planck-Institut für Mathematik, Bonn Garbe Mathematik (DE-588)4019261-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Modulraum (DE-588)4183462-8 gnd |
| subject_GND | (DE-588)4019261-1 (DE-588)4001161-6 (DE-588)4183462-8 |
| title | The geometry of moduli spaces of sheaves a publication of the Max-Planck-Institut für Mathematik, Bonn |
| title_auth | The geometry of moduli spaces of sheaves a publication of the Max-Planck-Institut für Mathematik, Bonn |
| title_exact_search | The geometry of moduli spaces of sheaves a publication of the Max-Planck-Institut für Mathematik, Bonn |
| title_full | The geometry of moduli spaces of sheaves a publication of the Max-Planck-Institut für Mathematik, Bonn Daniel Huybrechts ; Manfred Lehn |
| title_fullStr | The geometry of moduli spaces of sheaves a publication of the Max-Planck-Institut für Mathematik, Bonn Daniel Huybrechts ; Manfred Lehn |
| title_full_unstemmed | The geometry of moduli spaces of sheaves a publication of the Max-Planck-Institut für Mathematik, Bonn Daniel Huybrechts ; Manfred Lehn |
| title_short | The geometry of moduli spaces of sheaves |
| title_sort | the geometry of moduli spaces of sheaves a publication of the max planck institut fur mathematik bonn |
| title_sub | a publication of the Max-Planck-Institut für Mathematik, Bonn |
| topic | Garbe Mathematik (DE-588)4019261-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Modulraum (DE-588)4183462-8 gnd |
| topic_facet | Garbe Mathematik Algebraische Geometrie Modulraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007545028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018737 |
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