環(huán)簇（影印版）簡(jiǎn)介，目錄書(shū)摘

編輯推薦:

內容簡(jiǎn)介:　　環(huán)簇構成了現代代數幾何中優(yōu)美且易于理解的一部分。
　　《環(huán)簇（影印版）》涵蓋了環(huán)幾何中的標準主題，一個(gè)顯著(zhù)特色是前九章的每一章都包含了導引，用于交待代數幾何中必要的背景知識。
　　《環(huán)簇（影印版）》涵蓋的其他主題包括商構造、消逝定理、等變上同調、GIT商、次要扇及針對環(huán)簇的極小模型綱領(lǐng)。環(huán)簇有豐富的例子，這反映在書(shū)中的134幅插圖中。
　　《環(huán)簇（影印版）》同樣探究了交換代數與多面體幾何的聯(lián)系，討論了多胞體及其無(wú)界的孿生體一一多面體。書(shū)后有兩個(gè)附錄，分別介紹了環(huán)簇的歷史和用以考察環(huán)幾何中非平凡例子的計算工具。
　　《環(huán)簇（影印版）》讀者應熟悉研究生基礎課程所涉及的代數和拓撲知識，以及程度略低一點(diǎn)的復分析知識。此外，作者假定讀者具備一定程度的高年級本科生水平的代數幾何知識。
　　《環(huán)簇（影印版）》對于對代數幾何、多面體幾何和環(huán)簇感興趣的研究生和研究人員是一本好參考書(shū)。

作者簡(jiǎn)介:

目錄:Preface
Notation

Part I． Basic Theory of Toric Varieties
Chapter 1． Affine Toric Varieties
1．0．Background： Affine Varieties
1，1， Introduction to Affine Toric Varieties
1．2． Cones and Affine Toric Varieties
1．3． Properties of Affine Toric Varieties
Appendix： Tensor Products of Coordinate Rings
Chapter 2． Projective Toric Varieties
2．0． Background： Projective Varieties
2．1． Lattice Points and Projective Toric Varieties
2．2． Lattice Points and Polytopes
2．3． Polytopes and Projective Toric Varieties
2．4． Properties of Projective Toric Varieties
Chapter 3． Normal Toric Varieties
3．0． Background： Abstract Varieties
3．1．Fans and Normal Toric Varieties
3．2． The Orbit-Cone Correspondence
3．3． Toric Morphisms
3．4． Complete and Proper
Appendix： Nonnormal Toric Varieties
Chapter 4． Divisors on Toric Varieties
4．0．Background： Valuations， Divisors and Sheaves
4．1． Weil Divisors on Toric Varieties
4．2． Cartier Divisors on Toric Varieties
4．3． The Sheafofa Torus-Invariant Divisor
Chapter 5． Homogeneous Coordinates on Toric Varieties
5．0．Background： Quotients in Algebraic Geometry
5．1． Quotient Constructions of Toric Varieties
5．2． The Total Coordinate Ring
5．3． Sheaves on Toric Varieties
5．4． Homogenization and Polytopes
Chapter 6． Line Bundles on Toric Varieties
6．0． Background： Sheaves and Line Bundles
6．1． Ample and Basepoint Free Divisors on Complete Toric Varieties
6．2． Polytopes and Projective Toric Varieties
6．3．The Nefand Mori Cones
6．4．The Simplicial Case
Appendix： Quasicoherent Sheaves on Toric Varieties
Chapter 7． Projective Toric Morphisms
7．0． Background： Quasiprojective Varieties and Projective Morphisms
7．1． Polyhedra and Toric Varieties
7．2． Projective Morphisms and Toric Varieties
7．3． Projective Bundles and Toric Varieties
Appendix： More on Projective Morphisms
Chapter 8．The Canonical Divisor ofa Toric Variety
8．0． Background： Refiexive Sheaves and Differential Forms
8．1． One-Forms on Toric Varieties
8．2．Differential Forms on Toric Varieties
8．3． Fano Toric Varieties
Chapter 9． Sheaf Cohomology of Toric Varieties
……

Part II． Topics in Toric Geometry

Appendix
Bibliography
Index