The geometry of moduli spaces of sheaves:
"Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, UK
Cambridge Univ. Press
2010
|
| Edition: | 2. ed. |
| Series: | Cambridge mathematical library
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points on surfaces, derived categories of coherent sheaves, and moduli spaces of sheaves on Calabi-Yau threefolds. The authors review changes in the field since the publication of the original edition in 1997 and point the reader towards further literature. References have been brought up to date and errors removed. Developed from the authors' lectures, this book is ideal as a text for graduate students as well as a valuable resource for any mathematician with a background in algebraic geometry who wants to learn more about Grothendieck's approach"--Provided by publisher. |
| Physical Description: | XVIII, 325 S. |
Staff View
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| 245 | 1 | 0 | |a The geometry of moduli spaces of sheaves |c Daniel Huybrechts and Manfred Lehn |
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Record in the Search Index
| _version_ | 1804141164576636928 |
|---|---|
| adam_text | Titel: The geometry of moduli spaces of sheaves
Autor: Huybrechts, Daniel
Jahr: 2010
Contents
Preface to the second edition page ix
Preface to thefirst edition xi
Introduction xiii
Part I General Theory 1
1 Preliminaries 3
1.1 Some Homological Algebra 3
1.2 Semistable Sheaves 10
1.3 The Harder-Narasimhan Filtration 15
1.4 AnExample 20
1.5 Jordan-Hölder Filtration and S-Equivalence 23
1.6 /z-Semistability 25
1.7 Boundednessl 29
2 Families of Sheaves 34
2.1 Fiat Families and Determinants 34
2.2 Grothendieck s Quot-Scheme 40
2.3 The Relative Harder-Narasimhan Filtration 48
Appendix
2. A Flag-Schemes and Deformation Theory 51
2.B AResultof Langton 58
2.C Further comments (second edition) 61
3 The Grauert-Mülich Theorem 63
3.1 Statement and Proof 64
3.2 Finite Coverings and Tensor Products 69
Contents
3.3 Boundedness II 75
3.4 The Bogomolov Inequality 79
Appendix
3.A e-Stability and Some Estimates 82
3.B Further comments (second edition) 87
Moduli Spaces 89
4.1 The Moduli Functor 90
4.2 Group Actions 91
4.3 The Construction ? Results 98
4.4 The Construction ? Proofs 104
4.5 Local Properties and Dimension Estimates 112
4.6 Universal Families 117
Appendix
4.A Gieseker s Construction 121
4.B Decorated Sheaves 122
4.C Change of Polarization 126
4.D Further comments (second edition) 132
Part II Sheaves on Surfaces 141
Construction Methods 143
5.1 The Serre Correspondence 145
5.2 Elementary Transformations 151
5.3 Examples of Moduli Spaces 154
Appendix
5.A Further comments (second edition) 164
Moduli Spaces on K3 Surfaces 166
6.1 Low-Dimensional... 167
6.2 ... and Higher-Dimensional Moduli Spaces 175
Appendix
6.A The Irreducibility of the Quot-scheme 184
6.B Further comments (second edition) 187
Restriction of Sheaves to Curves 193
7.1 Flenner s Theorem 193
7.2 The Theorems of Mehta and Ramanathan 197
7.3 Bogomolov s Theorems 204
Contents vii
Appendix
7.A Further comments (second edition) 212
8 Line Bundles on the Moduli Space 213
8.1 Construction of Determinant Line Bundles 213
8.2 A Moduli Space for //-Semistable Sheaves 220
8.3 The Canonical Class of the Moduli Space 232
8.4 Further comments (second edition) 236
9 Irreducibility and Smoothness 239
9.1 Preparations 239
9.2 TheBoundary 241
9.3 Generic Smoothness 242
9.4 Irreducibility 243
9.5 Proofof Theorem 9.2.2 245
9.6 Proofof Theorem 9.3.2 251
10 Symplectic Structures 255
10.1 Trace Map, Atiyah Class and Kodaira-Spencer Map 256
10.2 The Tangent Bündle 262
10.3 Forms on the Moduli Space 264
10.4 Non-Degeneracy of Two-Forms 267
Appendix
10.A Further comments (second edition) 271
11 Birational properties 272
11.1 Kodaira Dimension of Moduli Spaces 272
11.2 More Results 277
11.3 Examples 281
Appendix
11 .A Further comments (second edition) 287
References 290
Glossary of Notations 316
Index 321
|
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| edition | 2. ed. |
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| indexdate | 2024-07-09T22:11:31Z |
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| language | English |
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| spelling | Huybrechts, Daniel 1966- (DE-588)113483716 aut The geometry of moduli spaces of sheaves Daniel Huybrechts and Manfred Lehn 2. ed. Cambridge, UK Cambridge Univ. Press 2010 XVIII, 325 S. txt rdacontent n rdamedia nc rdacarrier Cambridge mathematical library "Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points on surfaces, derived categories of coherent sheaves, and moduli spaces of sheaves on Calabi-Yau threefolds. The authors review changes in the field since the publication of the original edition in 1997 and point the reader towards further literature. References have been brought up to date and errors removed. Developed from the authors' lectures, this book is ideal as a text for graduate students as well as a valuable resource for any mathematician with a background in algebraic geometry who wants to learn more about Grothendieck's approach"--Provided by publisher. Moduli theory Sheaf theory Surfaces, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Garbe Mathematik (DE-588)4019261-1 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 DE-604 Lehn, Manfred aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018988115&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huybrechts, Daniel 1966- Lehn, Manfred The geometry of moduli spaces of sheaves Moduli theory Sheaf theory Surfaces, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd Garbe Mathematik (DE-588)4019261-1 gnd Modulraum (DE-588)4183462-8 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4019261-1 (DE-588)4183462-8 |
| title | The geometry of moduli spaces of sheaves |
| title_auth | The geometry of moduli spaces of sheaves |
| title_exact_search | The geometry of moduli spaces of sheaves |
| title_full | The geometry of moduli spaces of sheaves Daniel Huybrechts and Manfred Lehn |
| title_fullStr | The geometry of moduli spaces of sheaves Daniel Huybrechts and Manfred Lehn |
| title_full_unstemmed | The geometry of moduli spaces of sheaves Daniel Huybrechts and Manfred Lehn |
| title_short | The geometry of moduli spaces of sheaves |
| title_sort | the geometry of moduli spaces of sheaves |
| topic | Moduli theory Sheaf theory Surfaces, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd Garbe Mathematik (DE-588)4019261-1 gnd Modulraum (DE-588)4183462-8 gnd |
| topic_facet | Moduli theory Sheaf theory Surfaces, Algebraic Algebraische Geometrie Garbe Mathematik Modulraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018988115&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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