Introduction to singularities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Japanese |
| Published: |
Tokyo
Springer
2018
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | x, 236 Seiten Diagramme 23.5 cm x 15.5 cm |
| ISBN: | 9784431568360 4431568360 |
Staff View
MARC
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| 240 | 1 | 0 | |a Tokuiten Nyûmon |
| 245 | 1 | 0 | |a Introduction to singularities |c Shihoko Ishii |
| 250 | |a Second edition | ||
| 264 | 1 | |a Tokyo |b Springer |c 2018 | |
| 264 | 4 | |c © 2018 | |
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| 653 | |a Classification of singularities | ||
| 653 | |a Mixed Hodge structure | ||
| 653 | |a Resolution | ||
| 653 | |a Singularities | ||
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Record in the Search Index
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|---|---|
| adam_text |
Contents
1 Warming Up. 1
1.1 By Cutting — Hypersurface Singularity, Hypersurface
Cut of a Singularity. 3
1.2 By Dividing — Quotient Singularity, Quotient
of a Singularity. 4
1.3 By Lifting Up — Covering Singularity . 4
1.4 By Contracting. 5
2 Sheaves, Algebraic Varieties and Analytic Spaces. 7
2.1 Preliminaries on Category. . . 7
2.2 Sheaves on a Topological Space . . . 14
2.3 Analytic Spaces, Algebraic Varieties . 19
2.4 Coherent Sheaves. 23
3 Homological Algebra and Duality. 27
3.1 Injective Resolution . 27
3.2 ith Derived Functor. 35
3.3 Ext. . 38
3.4 Sheaf Cohomologies . 42
3.5 Derived Functors and Duality . . . 45
3.6 Spectral Sequences . 49
4 Definition of a Singularity, Resolutions of Singularities. 55
4.1 Definition of a Singularity . 55
4.2 Algebraization Theorem . 61
4.3 Resolutions of Singularities and Blow-Up. 63
4.4 Toric Resolutions of Singularities . 69
ix
x Contents
5 Divisors and Sheaves on a Variety . . . . . . . .'. . . . . . . . . . 81
5.1 Locally Free Sheaves, Invertible Sheaves, Divisorial
Sheaves . . . . . . . . . . . . . . . . 81
5.2 Divisors . . . . . . . . . . . . . . . . . . . . 85
5.3 Canonical Sheaf and Canonical Divisor. . 89
5.4 Intersection Number of Divisors . . 96
6 Differential Forms Around a Singularity. . 99
6.1 Ramification Formula . . . . . . . . . . . 99
6.2 Canonical, Terminal, Rational Singularities . . . . . . . . . 105
6.3 Classification of Normal Isolated Singularities . . . 113
7 Normal 2-Dimensional Singularities. 119
7.1 Resolutions of Singularities on a Surface . . . . . . . . . . . .119
7.2 The Fundamental Cycle. . . . . . . . . 127
7.3 Rational Singularities. ./. . 132
7.4 Quotient Singularities . . . . . . . . . . . . . . . 138
7.5 Rational Double Point. 147
7.6 Elliptic Singularities . . . . . 151
7.7 2-Dimensional Du Bois Singularities . 153
7.8 Classification of 2-Dimensional Singularities by Ks . . . . . 158
8 Higher-Dimensional Singularities . 161
8.1 Mixed Hodge Structure and Du Bois Singularities . . 161
8.2 Minimal Model Problem . . . . . . . . . . . . . . . . . . . 171
8.3 Higher-Dimensional Canonical Singularities, Terminal
Singularities . . . . . . . . . 176
8.4 Higher-Dimensional Isolated 1-Gorenstein Singularities. . . . 186
9 Deformations of Singularities . . . . . . . . . . . . . . . . 199
9.1 Variation of Properties Under Deformations . . . . . . . . . . . 199
9.2 Semi-universal Deformations. . . . 209
10 Quick Overview of Recent Developments on Singularities . 213
10.1 Thinking of Pairs and the Log Discrepancies . . . . . . . . . . . . . 213
10.2 The Spaces of Jets and Arcs . . . . . . . . _ . . . 218
10.3 F-Singularities in Positive Characteristic . . . . . . . . . 223
References. . . . . . . . 227
Index . . . . . . . V . . . 233 |
| any_adam_object | 1 |
| author | Ishii, Shihoko |
| author_GND | (DE-588)1063112087 |
| author_facet | Ishii, Shihoko |
| author_role | aut |
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| bvnumber | BV045222787 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)1057678224 (DE-599)DNB1156028906 |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| indexdate | 2025-03-16T07:00:26Z |
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| language | English Japanese |
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| spelling | Ishii, Shihoko Verfasser (DE-588)1063112087 aut Tokuiten Nyûmon Introduction to singularities Shihoko Ishii Second edition Tokyo Springer 2018 © 2018 x, 236 Seiten Diagramme 23.5 cm x 15.5 cm txt rdacontent n rdamedia nc rdacarrier Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Canonical divisors Classification of singularities Mixed Hodge structure Resolution Singularities (DE-588)4151278-9 Einführung gnd-content Singularität Mathematik (DE-588)4077459-4 s DE-604 Springer Japan KK (DE-588)1065501234 pbl Erscheint auch als Online-Ausgabe 978-4-431-56837-7 Vorangegangen ist 9784431550808 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5b8b47edae4c46dcbe8927ba6bed7735&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030611351&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ishii, Shihoko Introduction to singularities Singularität Mathematik (DE-588)4077459-4 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4151278-9 |
| title | Introduction to singularities |
| title_alt | Tokuiten Nyûmon |
| title_auth | Introduction to singularities |
| title_exact_search | Introduction to singularities |
| title_full | Introduction to singularities Shihoko Ishii |
| title_fullStr | Introduction to singularities Shihoko Ishii |
| title_full_unstemmed | Introduction to singularities Shihoko Ishii |
| title_short | Introduction to singularities |
| title_sort | introduction to singularities |
| topic | Singularität Mathematik (DE-588)4077459-4 gnd |
| topic_facet | Singularität Mathematik Einführung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=5b8b47edae4c46dcbe8927ba6bed7735&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030611351&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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