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Introduction to Toric Varieties


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Table of Contents

Ch. 1Definitions and examples1.1Introduction31.2Convex polyhedral cones81.3Affine toric varieties151.4Fans and toric varieties201.5Toric varieties from polytopes23Ch. 2Singularities and compactness2.1Local properties of toric varieties282.2Surfaces; quotient singularities312.3One-parameter subgroups; limit points362.4Compactness and properness392.5Nonsingular surfaces422.6Resolution of singularities45Ch. 3Orbits, topology, and line bundles3.1Orbits513.2Fundamental groups and Euler characteristics563.3Divisors603.4Line bundles633.5Cohomology of line bundles73Ch. 4Moment maps and the tangent bundle4.1The manifold with singular corners784.2Moment map814.3Differentials and the tangent bundle854.4Serre duality874.5Betti numbers91Ch. 5Intersection theory5.1Chow groups965.2Cohomology of nonsingular toric varieties1015.3Riemann-Roch theorem1085.4Mixed volumes1145.5Bezout theorem1215.6Stanley's theorem124Notes131References149Index of Notation151Index155

About the Author

William Fulton is Professor of Mathematics at the University of Chicago.

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