环簇构成了现代代数几何中优美且易于理解的一部分。戴维·A·考克斯、约翰·B·利特、亨利·K·申克著的《环簇(英文版)(精)》涵盖了环几何中的标准主题，一个显著特色是前九章的每一章都包含了导引，用于交待代数几何中必要的背景知识。本书涵盖的其他主题包括商构造、消逝定理、等变上同调、GIT商、次要扇及针对环簇的极小模型纲领。环簇有丰富的例子，这反映在书中的134幅插图中。本书同样探究了交换代数与多面体几何的联系，讨论了多胞体及其无界的孪生体——多面体。书后有两个附录，分别介绍了环簇的历史和用以考察环几何中非平凡例子的计算工具。
本书读者应熟悉研究生基础课程所涉及的代数和拓扑知识，以及程度略低一点的复分析知识。此外，作者假定读者具备一定程度的高年级本科生水平的代数几何知识。本书对于对代数几何、多面体几何和环簇感兴趣的研究生和研究人员是一本极佳的参考书。

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 ofAffine 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 Sheaf of a 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. TheNefandMori 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 Torie 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 of a Toric Variety
8.0. Background: Reflexive 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
9.0. Background: SheafCohomology
9.1. Cohomology of Toric Divisors
9.2. Vanishing Theorems I
9.3. Vanishing Theorems II
9.4. Lattice Polytopes and Differential Forms
9.5. Local Cohomology and the Total Coordinate Ring
Part II. Topics in Toric Geometry
Chapter 10. Toric Surfaces
10.1. Singularities of Toric Surfaces and Their Resolutions
10.2. Continued Fractions and Toric Surfaces
10.3. Grobner Fans and MCKay Correspondences
10.4. Smooth Toric Surfaces
10.5. Riemann-Roch and Lattice Polygons
Chapter 11. Toric Resolutions and Toric Singularities
11.1. Resolution of Singularities
11.2. Other Types of Resolutions
11.3. Rees Algebras and Multiplier Ideals
11.4. Toric Singularities
Chapter 12. The Topology of Toric Varieties
12.1. The Fundamental Group
12.2. The Moment Map
12.3. Singular Cohomology of Toric Varieties
12.4. The Cohomology Ring
12.5. The Chow Ring and Intersection Cohomology
Chapter 13. Toric Hirzebruch-Riemann-Roch
13.1. Chern Characters, Todd Classes, and HRR
13.2. Brion's Equalities
13.3. Toric Equivariant Riemann-Roch
13.4. The Volume Polynomial
13.5. The Khovanskii-Pukhlikov Theorem
Appendix: Generalized Gysin Maps
Chapter 14. Toric GIT and the Secondary Fan
14.1. Introduction to Toric GIT
14.2. Toric GIT and Polyhedra
14.3. Toric GIT and Gale Duality
14.4. The Secondary Fan
Chapter 15. Geometry of the Secondary Fan
15.1. The Nef and Moving Cones
15.2. Gale Duality and Triangulations
15.3. Crossing a Wall