Combinatorial convexity and algebraic geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Schriftenreihe: | Graduate texts in mathematics
168 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 372 S. graph. Darst. |
| ISBN: | 0387947558 |
Internformat
MARC
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| 100 | 1 | |a Ewald, Günter |d 1929-2015 |e Verfasser |0 (DE-588)122336224 |4 aut | |
| 245 | 1 | 0 | |a Combinatorial convexity and algebraic geometry |c Günter Ewald |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XIV, 372 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 168 | |
| 650 | 4 | |a Combinatorial geometry | |
| 650 | 4 | |a Toric varieties | |
| 650 | 4 | |a Geometry, Algebraic | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface vii
Introduction xiii
Parti
Combinatorial Convexity
I. Convex Bodies 3
1. Convex sets 3
2. Theorems of Radon and Caratheodory 8
3. Nearest point map and supporting hyperplanes 11
4. Faces and normal cones 14
5. Support function and distance function 18
6. Polar bodies 24
II. Combinatorial theory of polytopes and polyhedral sets 29
1. The boundary complex of a polyhedral set 29
2. Polar polytopes and quotient polytopes 35
3. Special types of polytopes 40
4. Linear transforms and Gale transforms 45
5. Matrix representation of transforms 53
6. Classification of polytopes 58
III. Polyhedral spheres 65
1. Cell complexes 65
2. Stellar operations 70
3. The Euler and the Dehn Sommerville equations 78
4. Schlegel diagrams, n diagrams, and polytopality of spheres 84
5. Embedding problems 88
6. Shellings 92
x Contents
7. Upper bound theorem 96
IV. Minkowski sum and mixed volume 103
1. Minkowski sum 103
2. Hausdorff metric 107
3. Volume and mixed volume 115
4. Further properties of mixed volumes 120
5. Alexandrov Fenchel s inequality 129
6. Ehrhart s theorem 135
7. Zonotopes and arrangements of hyperplanes 138
V. Lattice poly topes and fans 143
1. Lattice cones 143
2. Dual cones and quotient cones 148
3. Monoids 154
4. Fans 158
5. The combinatorial Picard group 167
6. Regular stellar operations 179
7. Classification problems 186
8. Fano polytopes 192
Part 2
Algebraic Geometry
VI. Toric varieties 199
1. Ideals and affine algebraic sets 199
2. Affine toric varieties 214
3. Toric varieties 224
4. Invariant toric subvarieties 234
5. The torus action 238
6. Toric morphisms and fibrations 242
7. Blowups and blowdowns 248
8. Resolution of singularities 252
9. Completeness and compactness 257
VII. Sheaves and projective toric varieties 259
1. Sheaves and divisors 259
2. Invertible sheaves and the Picard group 267
3. Projective toric varieties 273
4. Support functions and line bundles 281
5. Chow ring 287
6. Intersection numbers. Hodge inequality 290
Contents xi
7. Moment map and Morse function 296
8. Classification theorems. Toric Fano varieties 303
VIII. Cohomology of toric varieties 307
1. Basic concepts 307
2. Cohomology ring of a toric variety 314
3. Cech cohomology 317
4. Cohomology of invertible sheaves 320
5. The Riemann Roch Hirzebruch theorem 324
Summary: A Dictionary 329
Appendix
Comments, historical notes, further exercises, research
problems, suggestions for further reading 331
References 343
List of Symbols 359
Index 363
|
| any_adam_object | 1 |
| author | Ewald, Günter 1929-2015 |
| author_GND | (DE-588)122336224 |
| author_facet | Ewald, Günter 1929-2015 |
| author_role | aut |
| author_sort | Ewald, Günter 1929-2015 |
| author_variant | g e ge |
| building | Verbundindex |
| bvnumber | BV011059203 |
| callnumber-first | Q - Science |
| callnumber-label | QA639 |
| callnumber-raw | QA639.5.E93 1996 |
| callnumber-search | QA639.5.E93 1996 |
| callnumber-sort | QA 3639.5 E93 41996 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 |
| classification_tum | MAT 525f MAT 140f |
| ctrlnum | (OCoLC)246650064 (DE-599)BVBBV011059203 |
| dewey-full | 516.08 516/.0820 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.08 516/.08 20 |
| dewey-search | 516.08 516/.08 20 |
| dewey-sort | 3516.08 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:03:18Z |
| institution | BVB |
| isbn | 0387947558 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007406524 |
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| physical | XIV, 372 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Ewald, Günter 1929-2015 Verfasser (DE-588)122336224 aut Combinatorial convexity and algebraic geometry Günter Ewald New York [u.a.] Springer 1996 XIV, 372 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 168 Combinatorial geometry Toric varieties Geometry, Algebraic Torus (DE-588)4185738-0 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Toruseinbettung (DE-588)4194508-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Kombinatorische Geometrie (DE-588)4140733-7 s Torus (DE-588)4185738-0 s DE-604 Toruseinbettung (DE-588)4194508-6 s Graduate texts in mathematics 168 (DE-604)BV000000067 168 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007406524&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ewald, Günter 1929-2015 Combinatorial convexity and algebraic geometry Graduate texts in mathematics Combinatorial geometry Toric varieties Geometry, Algebraic Torus (DE-588)4185738-0 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Toruseinbettung (DE-588)4194508-6 gnd |
| subject_GND | (DE-588)4185738-0 (DE-588)4140733-7 (DE-588)4001161-6 (DE-588)4194508-6 |
| title | Combinatorial convexity and algebraic geometry |
| title_auth | Combinatorial convexity and algebraic geometry |
| title_exact_search | Combinatorial convexity and algebraic geometry |
| title_full | Combinatorial convexity and algebraic geometry Günter Ewald |
| title_fullStr | Combinatorial convexity and algebraic geometry Günter Ewald |
| title_full_unstemmed | Combinatorial convexity and algebraic geometry Günter Ewald |
| title_short | Combinatorial convexity and algebraic geometry |
| title_sort | combinatorial convexity and algebraic geometry |
| topic | Combinatorial geometry Toric varieties Geometry, Algebraic Torus (DE-588)4185738-0 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Toruseinbettung (DE-588)4194508-6 gnd |
| topic_facet | Combinatorial geometry Toric varieties Geometry, Algebraic Torus Kombinatorische Geometrie Algebraische Geometrie Toruseinbettung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007406524&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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