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组合凸性和代数几何PDF|Epub|txt|kindle电子书版本网盘下载

组合凸性和代数几何
  • 埃瓦尔德（GunterEwald）著 著
  • 出版社： 世界图书出版公司北京公司
  • ISBN：9787510037566
  • 出版时间：2011
  • 标注页数：374页
  • 文件大小：50MB
  • 文件页数：389页
  • 主题词：凸体－英文；代数几何－英文

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图书目录

Part 1 Combinatorial Convexity3

Ⅰ．Convex Bodies3

1．Convex sets3

2．Theorems of Radon and Carathéodory8

3．Nearest point map and supporting hyperplanes11

4．Faces and normal cones14

5．Support function and distance function18

6．Polar bodies24

Ⅱ．Combinatorial theory of polytopes and polyhedral sets29

1．The boundary complex of a polyhedral set29

2．Polar polytopes and quotient polytopes35

3．Special types of polytopes40

4．Linear transforms and Gale transforms45

5．Matrix representation of transforms53

6．Classification of polytopes58

Ⅲ．Polyhedral spheres65

1．Cell complexes65

2．Stellar operations70

3．The Euler and the Dehn-Sommerville equations78

4．Schlegel diagrams,n-diagrams,and polytopality of spheres84

5．Embedding problems88

6．Shellings92

7．Upper bound theorem96

Ⅳ．Minkowski sum and mixed volume103

1．Minkowski sum103

2．Hausdorff metric107

3．Volume and mixed volume115

4．Further properties of mixed volumes120

5．Alexandrov-Fenchel's inequality129

6．Ehrhart's theorem135

7．Zonotopes and arrangements of hyperplanes138

Ⅴ ．Lattice polytopes and fans143

1．Lattice cones143

2．Dual cones and quotient cones148

3．Monoids154

4．Fans158

5．The combinatorial Picard group167

6．Regular stellar operations179

7．Classification problems186

8．Fano polytopes192

Part 2 Algebraic Geometry199

Ⅵ．Toric varieties199

1．Ideals and affine algebraic sets199

2．Affine toric varieties214

3．Toric varieties224

4．Invariant toric subvarieties234

5．The torus action238

6．Toric morphisms and fibrations242

7．Blowups and blowdowns248

8．Resolution of singularities252

9．Completeness and compactness257

Ⅶ．Sheaves and projective toric varieties259

1．Sheaves and divisors259

2．Invertible sheaves and the Picard group267

3．Projective toric varieties273

4．Support functions and line bundles281

5．Chow ring287

6．Intersection numbers.Hodge inequality290

7．Moment map and Morse function296

8．Classification theorems.Toric Fano varieties303

Ⅷ．Cohomology of toric varieties307

1．Basic concepts307

2．Cohomology ring of a toric variety314

3．？ech cohomology317

4．Cohomology of invertible sheaves320

5．The Riemann-Roch-Hirzebruch theorem324

Summary:A Dictionary329

Appendix Comments,historical notes,further exercises,research problems,suggestions for further reading331

References343

List of Symbols359

Index363

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