Geometry of the Noether-Lefschetz locus:
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| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
2015
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 111 Seiten |
Internformat
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Datensatz im Suchindex
| _version_ | 1804175891065995264 |
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| adam_text | CONTENTS
SELBSTANDIGKEITSERKLARUNG I
SUMMARY III
ZUSAMMENFASSUNG V
ACKNOWLEDGEMENTS VII
CONTENTS IX
NOTATIONS XI
1 INTRODUCTION 1
1.1 NOETHER-LEFSCHETZ LOCUS 1
1.2 KNOWN RESULTS 2
1.3 NEW RESULTS 3
2 PREREQUISITES 5
2.1 VARIATION OF HODGE STRUCTURES 5
2.1.1 KODAIRA-SPENCER MAP 6
2.1.2 GAUSS-MANIN CONNECTION 8
2.1.3 PERIOD MAPS 9
2.1.4 HODGE BUNDLE 13
2.1.5 TRANSVERSALITY 14
2.1.6 STUDY OF THE HODGE LOCUS 16
2.2 REDUCTION TO COMMUTATIVE ALGEBRA 17
2.3 NON-REDUCED SCHEMES 20
2.4 TANGENT AND NORMAL SHEAVES 21
2.5 FLAG HILBERT SCHEME AND HODGE LOCUS 23
2.6 BLOCH S SEMIREGULARITY MAP FOR DIVISORS 24
2.7 CASTELNUOVO-MUMFORD REGULARITY 30
IX
HTTP://D-NB.INFO/1080150285
CONTENTS X
2.8 NOETHER-LEFSCHETZ LOCUS FOR HYPERSURFACES IN P
2N+1
31
3 NON-REDUCED COMPONENTS OF THE NOETHER-LEFSCHETZ LOCUS 37
3.1 INTRODUCTION 37
3.2 HODGE LOCUS AND SEMI-REGULARITY 38
3.3 CRITERION FOR NON-REDUCEDNESS 41
3.4 EXAMPLES 46
3.4.1 A SMOOTH EXAMPLE 47
3.4.2 MARTIN-DESCHAMPS AND PERRIN S EXAMPLE 47
3.4.3 COMPUTING CASTELNUOVO-MUMFORD REGULARITY 47
3.4.4 EXAMPLES OF NON-REDUCED COMPONENTS OF NL^ 50
4 ON MUMFORD S EXAMPLE 53
4.1 INTRODUCTION 53
4.2 MUMFORD S EXAMPLE 55
4.3 GENERAL CRITERIA FOR NON-REDUCEDNESS 58
4.4 GENERALIZATION OF MUMFORD S EXAMPLE 60
5 HILBERT SCHEME OF D-EMBEDDED CURVES 65
5.1 INTRODUCTION 65
5.2 HILBERT SCHEME OF D-EMBEDDED CURVES 66
5.3 TANGENT SPACE TO HILBERT SCHEME OF D-EMBEDDED CURVES 70
5.4 ON AN EXAMPLE OF MARTIN-DESCHAMPS AND PERRIN 74
5.5 CHAIN RELATED CURVES AND INDUCED NON-REDUCEDNESS 79
5.6 EXAMPLES 84
5.6.1 TOPOLOGICAL INVARIANCE OF DIVISORS UNDER DEFORMATION 84
5.6.2 NORMAL SHORT EXACT SEQUENCES AND CHAIN RELATEDNESS OF CURVES 87
5.6.3 EXAMPLES OF NON-REDUCED COMPONENTS OF HILBERT SCHEME OF
D-EMBEDDED CURVES 90
6 GRIFFITHS-HARRIS CONJECTURE 95
6.1 INTRODUCTION 95
6.2 VARIATION OF LATTICES 96
6.3 A CONJECTURE OF GRIFFITHS AND HARRIS 98
7 ELEMENTARY TECHNIQUES 103
7.1 INTRODUCTION 103
7.2 PROOF OF THEOREM 7.1.2 104
7.3 PROOF OF THEOREM 7.1.3 107
BIBLIOGRAPHY 111
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| author | Dan, Ananyo |
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| ctrlnum | (OCoLC)956259554 (DE-599)BVBBV043340525 |
| discipline | Mathematik |
| format | Thesis Book |
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| spelling | Dan, Ananyo Verfasser (DE-588)108214553X aut Geometry of the Noether-Lefschetz locus von Ananyo Dan Berlin 2015 xi, 111 Seiten txt rdacontent n rdamedia nc rdacarrier Dissertation Humboldt-Universität zu Berlin 2015 (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028760438&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dan, Ananyo Geometry of the Noether-Lefschetz locus |
| subject_GND | (DE-588)4113937-9 |
| title | Geometry of the Noether-Lefschetz locus |
| title_auth | Geometry of the Noether-Lefschetz locus |
| title_exact_search | Geometry of the Noether-Lefschetz locus |
| title_full | Geometry of the Noether-Lefschetz locus von Ananyo Dan |
| title_fullStr | Geometry of the Noether-Lefschetz locus von Ananyo Dan |
| title_full_unstemmed | Geometry of the Noether-Lefschetz locus von Ananyo Dan |
| title_short | Geometry of the Noether-Lefschetz locus |
| title_sort | geometry of the noether lefschetz locus |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028760438&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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