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Combinatorial convexity and algebraic geometry:

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Bibliographic Details
Main Author:	Ewald, Günter 1929-2015 (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Springer 1996
Series:	Graduate texts in mathematics 168
Subjects:	Combinatorial geometry Toric varieties Geometry, Algebraic Torus Kombinatorische Geometrie Algebraische Geometrie Toruseinbettung
Links:	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
Physical Description:	XIV, 372 S. graph. Darst.
ISBN:	0387947558

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Record in the Search Index

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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
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isbn	0387947558
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series	Graduate texts in mathematics
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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
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT ewaldgunter combinatorialconvexityandalgebraicgeometry

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