Intersection theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
1998
|
| Edition: | Second edition |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete / 3
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 442 - 461 Softcoverausgabe außerhalb der Reihe erschienen |
| Physical Description: | XIII, 470 Seiten |
| ISBN: | 354062046X |
Staff View
MARC
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| 100 | 1 | |a Fulton, William |d 1939- |e Verfasser |0 (DE-588)136272541 |4 aut | |
| 245 | 1 | 0 | |a Intersection theory |c William Fulton |
| 250 | |a Second edition | ||
| 264 | 1 | |a New York, NY |b Springer |c 1998 | |
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| 300 | |a XIII, 470 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete / 3 |v 2 | |
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Record in the Search Index
| _version_ | 1804126199597760512 |
|---|---|
| adam_text | Contents
Introduction
Chapter 1. Rational Equivalence
Summary
1.1 Notation and Conventions
1.2 Orders of Zeros and Poles
1.3 Cycles and Rational Equivalence 10
1.4 Push forward of Cycles
1.5 Cycles of Subschemes
1.6 Alternate Definition of Rational Equivalence 15
1.7 Flat Pull back of Cycles 8
1.8 An Exact Sequence
1.9 Affine Bundles tt
1.10 Exterior Products Zl
Notes and References
JQ
Chapter 2. Divisors
Summary
2.1 Carder Divisors and Weil Divisors ^
2.2 Line Bundles and Pseudo divisors i]
2.3 Intersecting with Divisors ¦ . . •
2.4 Commutativity of Intersection Classes ¦ ¦
2.5 Chern Class of a Line Bundle *
2.6 Gysin Map for Divisors
Notes and References
Chapter 3. Vector Bundles and Chern Classes 47
c 47
Summary . ,
3.1 Segre Classes of Vector Bundles ^
3.2 Chern Classes . ,.
3.3 Rational Equivalence on Bundles ^
Notes and References
Chapter 4. Cones and Segre Classes
Summary ™
4.1 Segre Class of a Cone
X Contents
4.2 Segre Class of a Subscheme 73
4.3 Multiplicity Along a Subvariety 79
4.4 Linear Systems 82
Notes and References 85
Chapter 5. Deformation to the Normal Cone 86
Summary 86
5.1 The Deformation 86
5.2 Specialization to the Normal Cone 89
Notes and References 90
Chapter 6. Intersection Products 92
Summary 92
6.1 The Basic Construction 93
6.2 Refined Gysin Homomorphisms 97
6.3 Excess Intersection Formula 102
6.4 Commutativity 106
6.5 Functoriality 108
6.6 Local Complete Intersection Morphisms 112
6.7 Monoidal Transforms 114
Notes and References 117
Chapter 7. Intersection Multiplicities 119
Summary 119
7.1 Proper Intersections 119
7.2 Criterion for Multiplicity One 126
Notes and References 127
Chapter 8. Intersections on Non singular Varieties 130
Summary 130
8.1 Refined Intersections 130
8.2 Intersection Multiplicities 137
8.3 Intersection Ring 140
8.4 Bezout s Theorem (Classical Version) 144
Notes and References 151
Chapter 9. Excess and Residual Intersections 153
Summary 153
9.1 Equivalence of a Connected Component 153
9.2 Residual Intersection Theorem 160
9.3 Double Point Formula 165
Notes and References 171*
Contents XI
Chapter 10. Families of Algebraic Cycles 175
Summary 175
10.1 Families of Cycle Classes 176
10.2 Conservation of Number 180
10.3 Algebraic Equivalence 185
10.4 An Enumerative Problem 187
Notes and References 193
Chapter 11. Dynamic Intersections 195
Summary 195
11.1 Limits of Intersection Classes 196
11.2 Infinitesimal Intersection Classes 198
11.3 Limits and Distinguished Varieties 200
11.4 Moving Lemmas 205
Notes and References 209
Chapter 12. Positivity 210
Summary 210
12.1 Positive Vector Bundles 211
12.2 Positive Intersections 218
12.3 Refined Bezout Theorem 223
12.4 Intersection Multiplicities 227
Notes and References 234
Chapter 13. Rationality 235
Summary 235
Notes and References 241
Chapter 14. Degeneracy Loci and Grassmannians 242
Summary 242
14.1 Localized Top Chern Class 244
14.2 Gysin Formulas 247
14.3 Determinantal Formula 249
14.4 Thom Porteous Formula 254
14.5 Schur Polynomials 263
14.6 Grassmann Bundles 266
14.7 Schubert Calculus 271
Notes and References 278
Chapter 15. Riemann Roch for Non singular Varieties 280
Summary 280
15.1 Preliminaries 280
15.2 Grothendieck Riemann Roch Theorem 286
15.3 Riemann Roch Without Denominators 296
XII Contents
15.4 Blowing up Chern Classes 298
Notes and References 302
Chapter 16. Correspondences 305
Summary 305
16.1 Algebra of Correspondences 305
16.2 Irregular Fixed Points 315
Notes and References 318
Chapter 17. Bivariant Intersection Theory . 319
Summary 319
17.1 Bivariant Rational Equivalence Classes 320
17.2 Operations and Properties 322
17.3 Homology and Cohomology 324
17.4 Orientations 326
17.5 Monoidal Transforms 332
17.6 Residual Intersection Theorem 333
Notes and References 337
Chapter 18. Riemann Roch for Singular Varieties 339
Summary 339
18.1 Graph Construction 340
18.2 Riemann Roch for Quasi projective Schemes 348
18.3 Riemann Roch for Algebraic Schemes 353
Notes and References 368
Chapter 19. Algebraic, Homological and Numerical Equivalence . . . 370
Summary 370
19.1 Cycle Map 371
19.2 Algebraic and Topological Intersections . . 378
19.3 Equivalence on Non singular Varieties 385
Notes and References 391
Chapter 20. Generalizations 393
Summary 393
20.1 Schemes Over a Regular Base Scheme 393
20.2 Schemes Over a Dedekind Domain 397
20.3 Specialization 398
20.4 Tor and Intersection Products 401
20.5 Higher ^ theory 403
Notes and References 404
Appendix A. Algebra 406
Summary 406
A.1 Length 406
Contents XIII
A.2 Herbrand Quotients 407
A.3 Order Functions 411
A.4 Flatness 413
A.5 Koszul Complexes 414
A.6 Regular Sequences 416
A.7 Depth 418
A.8 Normal Domains 419
A.9 Determinantal Identities 419
Notes and References 425
Appendix B. Algebraic Geometry (Glossary) 426
B. 1 Algebraic Schemes 426
B.2 Morphisms 427
B.3 Vector Bundles 430
B.4 Carrier Divisors 431
B.5 Projective Cones and Bundles 432
B.6 Normal Cones and Blowing Up 435
B.7 Regular Imbeddings and l.c.i. Morphisms 437
B.8 Bundles on Imbeddable Schemes 439
B.9 General Position 440
Bibliography 442
Notation 462
Index 464
|
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| discipline | Mathematik |
| edition | Second edition |
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| indexdate | 2024-07-09T18:13:40Z |
| institution | BVB |
| isbn | 354062046X |
| language | English |
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| physical | XIII, 470 Seiten |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete / 3 |
| spelling | Fulton, William 1939- Verfasser (DE-588)136272541 aut Intersection theory William Fulton Second edition New York, NY Springer 1998 © 1998 XIII, 470 Seiten txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete / 3 2 Literaturverzeichnis: Seite 442 - 461 Softcoverausgabe außerhalb der Reihe erschienen Intersection theory Schnitttheorie (DE-588)4179890-9 gnd rswk-swf Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd rswk-swf Arithmetisches Mittel (DE-588)4143009-8 gnd rswk-swf Schnittmultiplizität (DE-588)4179893-4 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Schnitttheorie (DE-588)4179890-9 s DE-604 Schnittmultiplizität (DE-588)4179893-4 s Algebraische Mannigfaltigkeit (DE-588)4128509-8 s Arithmetisches Mittel (DE-588)4143009-8 s Algebraische Geometrie (DE-588)4001161-6 s Reproduziert als Fulton, William Intersection theory Second edition Springer, 1998 978-0-387-98549-7 (DE-604)BV020833062 3 Ergebnisse der Mathematik und ihrer Grenzgebiete 2 (DE-604)BV000899194 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007863362&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fulton, William 1939- Intersection theory Intersection theory Schnitttheorie (DE-588)4179890-9 gnd Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Arithmetisches Mittel (DE-588)4143009-8 gnd Schnittmultiplizität (DE-588)4179893-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4179890-9 (DE-588)4128509-8 (DE-588)4143009-8 (DE-588)4179893-4 (DE-588)4001161-6 |
| title | Intersection theory |
| title_auth | Intersection theory |
| title_exact_search | Intersection theory |
| title_full | Intersection theory William Fulton |
| title_fullStr | Intersection theory William Fulton |
| title_full_unstemmed | Intersection theory William Fulton |
| title_short | Intersection theory |
| title_sort | intersection theory |
| topic | Intersection theory Schnitttheorie (DE-588)4179890-9 gnd Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Arithmetisches Mittel (DE-588)4143009-8 gnd Schnittmultiplizität (DE-588)4179893-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Intersection theory Schnitttheorie Algebraische Mannigfaltigkeit Arithmetisches Mittel Schnittmultiplizität Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007863362&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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