Birational geometry of algebraic varieties:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1998
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
134 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | VIII, 254 S. graph. Darst. |
| ISBN: | 0521632773 9780521060226 9780521632775 |
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MARC
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| 100 | 1 | |a Kollár, János |d 1956- |0 (DE-588)113796277 |4 aut | |
| 245 | 1 | 0 | |a Birational geometry of algebraic varieties |c János Kollár ; Shigefumi Mori |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1998 | |
| 300 | |a VIII, 254 S. |b graph. Darst. | ||
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| 490 | 1 | |a Cambridge tracts in mathematics |v 134 | |
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Record in the Search Index
| _version_ | 1804126686924505088 |
|---|---|
| adam_text | Contents
Preface page vii
Introduction 1
1 Rational Curves and the Canonical Class 7
1.1 Finding Rational Curves when Kx is Negative 8
1.2 Finding Rational Curves when Kx is not Nef 16
1.3 The Cone of Curves of Smooth Varieties 18
1.4 Minimal Models of Surfaces 26
1.5 Ampleness Criteria 29
2 Introduction to the Minimal Model Program 36
2.1 Introduction to Mori s Program 37
2.2 Extensions of the Minimal Model Program 45
2.3 Singularities in the Minimal Model Program 50
2.4 The Kodaira Vanishing Theorem 62
2.5 Generalizations of the Kodaira Vanishing Theorem 67
3 Cone Theorems 74
3.1 Introduction to the Proof of the Cone Theorem 75
3.2 Basepoint free Theorem 78
3.3 The Cone Theorem 81
3.4 The Rationality Theorem 86
3.5 The Non vanishing Theorem 91
3.6 Relative versions 93
3.7 Running the MMP 96
3.8 Minimal and Canonical Models 106
4 Surface Singularities of the Minimal Model Program 111
4.1 Log Canonical Surface Singularities 112
v
vi Contents
4.2 Du Val Singularities 122
4.3 Simultaneous Resolution for Du Val Singularities 128
4.4 Elliptic Surface Singularities 136
4.5 Deformations of Hypersurface Singularities 144
5 Singularities of the Minimal Model Program 152
5.1 Rational Singularities 153
5.2 Log Terminal Singularities 158
5.3 Canonical and Terminal Threefold Singularities 164
5.4 Inversion of Adjunction 172
5.5 Duality Theory 179
6 Three dimensional Flops 187
6.1 Flips and Flops 188
6.2 Terminal Flops 192
6.3 Terminalization and Q factorialization 195
6.4 Canonical Flops 201
7 Semi stable Minimal Models 207
7.1 Semi stable MMP 208
7.2 Semi stable Reduction Theorem 214
7.3 Special Semi stable Flips 220
7.4 Semi stable Flips 224
7.5 Applications to Families of Surfaces 229
7.6 A Survey of Further Results 236
Bibliography 241
Index 249
|
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| classification_tum | MAT 146f MAT 142f |
| ctrlnum | (OCoLC)245816061 (DE-599)BVBBV012083718 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:21:24Z |
| institution | BVB |
| isbn | 0521632773 9780521060226 9780521632775 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008181859 |
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| physical | VIII, 254 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Kollár, János 1956- (DE-588)113796277 aut Birational geometry of algebraic varieties János Kollár ; Shigefumi Mori 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1998 VIII, 254 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 134 Hier auch später erschienene, unveränderte Nachdrucke Singularität <Mathematik> - Algebraische Mannigfaltigkeit - Birationale Geometrie Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd rswk-swf Birationale Geometrie (DE-588)4494748-3 gnd rswk-swf Birationale Geometrie (DE-588)4494748-3 s Algebraische Mannigfaltigkeit (DE-588)4128509-8 s DE-604 Mori, Shigefumi aut Cambridge tracts in mathematics 134 (DE-604)BV000000001 134 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008181859&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kollár, János 1956- Mori, Shigefumi Birational geometry of algebraic varieties Cambridge tracts in mathematics Singularität <Mathematik> - Algebraische Mannigfaltigkeit - Birationale Geometrie Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Birationale Geometrie (DE-588)4494748-3 gnd |
| subject_GND | (DE-588)4128509-8 (DE-588)4494748-3 |
| title | Birational geometry of algebraic varieties |
| title_auth | Birational geometry of algebraic varieties |
| title_exact_search | Birational geometry of algebraic varieties |
| title_full | Birational geometry of algebraic varieties János Kollár ; Shigefumi Mori |
| title_fullStr | Birational geometry of algebraic varieties János Kollár ; Shigefumi Mori |
| title_full_unstemmed | Birational geometry of algebraic varieties János Kollár ; Shigefumi Mori |
| title_short | Birational geometry of algebraic varieties |
| title_sort | birational geometry of algebraic varieties |
| topic | Singularität <Mathematik> - Algebraische Mannigfaltigkeit - Birationale Geometrie Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Birationale Geometrie (DE-588)4494748-3 gnd |
| topic_facet | Singularität <Mathematik> - Algebraische Mannigfaltigkeit - Birationale Geometrie Algebraische Mannigfaltigkeit Birationale Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008181859&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT kollarjanos birationalgeometryofalgebraicvarieties AT morishigefumi birationalgeometryofalgebraicvarieties |