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Introduction to Toric Varieties. (AM-131)
William Fulton

Book Description

TABLE OF CONTENTS:

Ch. 1Definitions and examples
1.1Introduction3
1.2Convex polyhedral cones8
1.3Affine toric varieties15
1.4Fans and toric varieties20
1.5Toric varieties from polytopes23
Ch. 2Singularities and compactness
2.1Local properties of toric varieties28
2.2Surfaces; quotient singularities31
2.3One-parameter subgroups; limit points36
2.4Compactness and properness39
2.5Nonsingular surfaces42
2.6Resolution of singularities45
Ch. 3Orbits, topology, and line bundles
3.1Orbits51
3.2Fundamental groups and Euler characteristics56
3.3Divisors60
3.4Line bundles63
3.5Cohomology of line bundles73
Ch. 4Moment maps and the tangent bundle
4.1The manifold with singular corners78
4.2Moment map81
4.3Differentials and the tangent bundle85
4.4Serre duality87
4.5Betti numbers91
Ch. 5Intersection theory
5.1Chow groups96
5.2Cohomology of nonsingular toric varieties101
5.3Riemann-Roch theorem108
5.4Mixed volumes114
5.5Bezout theorem121
5.6Stanley's theorem124
Notes131
References149
Index of Notation151
Index155

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File created: 7/11/2014

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