Introduction to the Mori program:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXIII, 478 S. graph. Darst. |
| ISBN: | 0387984658 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV012464468 | ||
| 003 | DE-604 | ||
| 005 | 20090902 | ||
| 007 | t | ||
| 008 | 990319s2002 d||| |||| 00||| eng d | ||
| 016 | 7 | |a 963753282 |2 DE-101 | |
| 020 | |a 0387984658 |9 0-387-98465-8 | ||
| 035 | |a (OCoLC)45532478 | ||
| 035 | |a (DE-599)BVBBV012464468 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 |a DE-384 |a DE-739 |a DE-19 |a DE-634 |a DE-83 |a DE-11 | ||
| 050 | 0 | |a QA564 | |
| 082 | 0 | |a 516.3/53 |2 21 | |
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 084 | |a 14Mxx |2 msc | ||
| 100 | 1 | |a Matsuki, Kenji |d 1958- |e Verfasser |0 (DE-588)123549418 |4 aut | |
| 245 | 1 | 0 | |a Introduction to the Mori program |c Kenji Matsuki |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2002 | |
| 300 | |a XXIII, 478 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 7 | |a Algebraïsche meetkunde |2 gtt | |
| 650 | 7 | |a Classification |2 rasuqam | |
| 650 | 7 | |a Geometria algébrica |2 larpcal | |
| 650 | 7 | |a Programme de Mori |2 rasuqam | |
| 650 | 7 | |a Variedades algébricas |2 larpcal | |
| 650 | 7 | |a Variété algébrique |2 rasuqam | |
| 650 | 4 | |a Algebraic varieties |x Classification theory | |
| 650 | 0 | 7 | |a Klassifikationstheorie |0 (DE-588)4164034-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Varietät |0 (DE-588)4581715-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Varietät |0 (DE-588)4581715-7 |D s |
| 689 | 0 | 1 | |a Klassifikationstheorie |0 (DE-588)4164034-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008458644&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008458644 | ||
Datensatz im Suchindex
| _version_ | 1804127104046989312 |
|---|---|
| adam_text | Contents
Preface v
List of Notation xiii
Introduction: The Tale of the Mori Program 1
1 Birational Geometry of Surfaces 9
1.1 Castelnuovo s Contractibility Criterion 10
1.2 Surfaces Whose Canonical Bundles Are Not Nef I 21
1.3 Surfaces Whose Canonical Bundles Are Not Nef II 36
1.4 Basic Properties of Mori Fiber Spaces in Dimension 2 42
1.5 Basic Properties of Minimal Models in Dimension 2 51
1.6 Basic Properties of Canonical Models in Dimension 2 75
1.7 The Enriques Classification of Surfaces 83
1.8 Birational Relation Among Surfaces 88
2 Logarithmic Category 109
2.1 Iitaka s Philosophy 110
2.2 Log Birational Geometry of Surfaces 118
3 Overview of the Mori Program 129
3.1 Minimal Model Program in Dimension 3 or Higher 131
3.2 Basic Properties of Mori Fiber Spaces in Dimension 3 or
Higher 141
3.3 Basic Properties of Minimal Models in Dimension 3 or Higher . 153
3.4 Birational Relations Among Minimal Models and Mori Fiber
Spaces in Dimension 3 or Higher 155
x Contents
3.5 Variations of the Mori Program 161
4 Singularities 163
4.1 Terminal Singularities 164
4.2 Canonical Singularities 168
4.3 Logarithmic Variations 173
4.4 Discrepancy and Singularities 179
4.5 Canonical Cover 183
4.6 Classification in Dimension 2 191
5 Vanishing Theorems 250
5.1 Kodaira Vanishing Theorem 251
5.2 Kawamata Viehweg Vanishing Theorem 259
6 Base Point Freeness of Adjoint Linear Systems 268
6.1 Relevance of Log Category to Base Point Freeness of Adjoint
Linear Systems 269
6.2 Base Point Freeness Theorem 272
6.3 Nonvanishing Theorem of Shokurov 279
7 Cone Theorem 286
7.1 Rationality Theorem and Boundedness of the Denominator . . 286
7.2 Cone Theorem 297
8 Contraction Theorem 301
8.1 Contraction Theorem 301
8.2 Contractions of Extremal Rays 306
8.3 Examples 309
9 Flip 317
9.1 Existence of Flip 318
9.2 Termination of Flips 322
10 Cone Theorem Revisited 324
10.1 Mori s Bend and Break Technique 325
10.2 A Proof in the Smooth Case After Mori 330
10.3 Lengths of Extremal Rays 332
11 Logarithmic Mori Program 338
11.1 Log Minimal Model Program in Dimension 3 or Higher .... 338
11.2 Log Minimal Models and Log Mori Fiber Spaces in Dimension
3 or Higher 342
11.3 Birational Relations Among Log Minimal Models and Log
Mori Fiber Spaces 345
Contents xi
12 Birational Relation among Minimal Models 349
12.1 Flops Among Minimal Models 350
12.2 Chamber Structure of Ample Cones of Minimal Models .... 358
12.3 The Number of Minimal Models Is Finite (?!) 363
13 Birational Relation Among Mori Fiber Spaces 368
13.1 Sarkisov Program 369
13.2 Termination of the Sarkisov Program 392
13.3 Applications 399
14 Birational Geometry of Toric Varieties 413
14.1 Cone Theorem and Contraction Theorem for Toric Varieties . . 413
14.2 Toric Extremal Contractions and Flips 425
14.3 Toric Canonical and Log Canonical Divisors 442
14.4 Toric Minimal Model Program 447
14.5 Toric Sarkisov Program 449
References 455
Index 469
|
| any_adam_object | 1 |
| author | Matsuki, Kenji 1958- |
| author_GND | (DE-588)123549418 |
| author_facet | Matsuki, Kenji 1958- |
| author_role | aut |
| author_sort | Matsuki, Kenji 1958- |
| author_variant | k m km |
| building | Verbundindex |
| bvnumber | BV012464468 |
| callnumber-first | Q - Science |
| callnumber-label | QA564 |
| callnumber-raw | QA564 |
| callnumber-search | QA564 |
| callnumber-sort | QA 3564 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)45532478 (DE-599)BVBBV012464468 |
| dewey-full | 516.3/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/53 |
| dewey-search | 516.3/53 |
| dewey-sort | 3516.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01825nam a2200481 c 4500</leader><controlfield tag="001">BV012464468</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090902 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">990319s2002 d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">963753282</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387984658</subfield><subfield code="9">0-387-98465-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)45532478</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012464468</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA564</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.3/53</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 240</subfield><subfield code="0">(DE-625)143226:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">14Mxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Matsuki, Kenji</subfield><subfield code="d">1958-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)123549418</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to the Mori program</subfield><subfield code="c">Kenji Matsuki</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXIII, 478 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Universitext</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Algebraïsche meetkunde</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Classification</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometria algébrica</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Programme de Mori</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Variedades algébricas</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Variété algébrique</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic varieties</subfield><subfield code="x">Classification theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Klassifikationstheorie</subfield><subfield code="0">(DE-588)4164034-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Varietät</subfield><subfield code="0">(DE-588)4581715-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische Varietät</subfield><subfield code="0">(DE-588)4581715-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Klassifikationstheorie</subfield><subfield code="0">(DE-588)4164034-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008458644&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008458644</subfield></datafield></record></collection> |
| id | DE-604.BV012464468 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:28:02Z |
| institution | BVB |
| isbn | 0387984658 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008458644 |
| oclc_num | 45532478 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-739 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 |
| owner_facet | DE-703 DE-384 DE-739 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 |
| physical | XXIII, 478 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Matsuki, Kenji 1958- Verfasser (DE-588)123549418 aut Introduction to the Mori program Kenji Matsuki New York [u.a.] Springer 2002 XXIII, 478 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Algebraïsche meetkunde gtt Classification rasuqam Geometria algébrica larpcal Programme de Mori rasuqam Variedades algébricas larpcal Variété algébrique rasuqam Algebraic varieties Classification theory Klassifikationstheorie (DE-588)4164034-2 gnd rswk-swf Algebraische Varietät (DE-588)4581715-7 gnd rswk-swf Algebraische Varietät (DE-588)4581715-7 s Klassifikationstheorie (DE-588)4164034-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008458644&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matsuki, Kenji 1958- Introduction to the Mori program Algebraïsche meetkunde gtt Classification rasuqam Geometria algébrica larpcal Programme de Mori rasuqam Variedades algébricas larpcal Variété algébrique rasuqam Algebraic varieties Classification theory Klassifikationstheorie (DE-588)4164034-2 gnd Algebraische Varietät (DE-588)4581715-7 gnd |
| subject_GND | (DE-588)4164034-2 (DE-588)4581715-7 |
| title | Introduction to the Mori program |
| title_auth | Introduction to the Mori program |
| title_exact_search | Introduction to the Mori program |
| title_full | Introduction to the Mori program Kenji Matsuki |
| title_fullStr | Introduction to the Mori program Kenji Matsuki |
| title_full_unstemmed | Introduction to the Mori program Kenji Matsuki |
| title_short | Introduction to the Mori program |
| title_sort | introduction to the mori program |
| topic | Algebraïsche meetkunde gtt Classification rasuqam Geometria algébrica larpcal Programme de Mori rasuqam Variedades algébricas larpcal Variété algébrique rasuqam Algebraic varieties Classification theory Klassifikationstheorie (DE-588)4164034-2 gnd Algebraische Varietät (DE-588)4581715-7 gnd |
| topic_facet | Algebraïsche meetkunde Classification Geometria algébrica Programme de Mori Variedades algébricas Variété algébrique Algebraic varieties Classification theory Klassifikationstheorie Algebraische Varietät |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008458644&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT matsukikenji introductiontothemoriprogram |