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Introduction to toric varieties

Author: William Fulton
Publisher: Princeton, N.J. : Princeton University Press, 1993.
Series: Annals of mathematics studies, no. 131.; William H. Roever lectures in geometry.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects. This text aims to develop the foundations of the study of toric varieties, and describe these  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: William Fulton
ISBN: 0691033323 9780691033327 0691000492 9780691000497
OCLC Number: 28066535
Description: xi, 157 pages : illustrations ; 25 cm.
Contents: Ch. 1. Definitions and examples --
1.1. Introduction. 1.2. Convex polyhedral cones. 1.3. Affine toric varieties. 1.4. Fans and toric varieties. 1.5. Toric varieties from polytopes --
Ch. 2. Singularities and compactness. 2.1. Local properties of toric varieties. 2.2. Surfaces; quotient singularities. 2.3. One-parameter subgroups; limit points. 2.4. Compactness and properness. 2.5. Nonsingular surfaces. 2.6. Resolution of singularities --
Ch. 3. Orbits, topology, and line bundles. 3.1. Orbits. 3.2. Fundamental groups and Euler characteristics. 3.3. Divisors. 3.4. Line bundles. 3.5. Cohomology of line bundles --
Ch. 4. Moment maps and the tangent bundle. 4.1. The manifold with singular corners. 4.2. Moment map. 4.3. Differentials and the tangent bundle. 4.4. Serre duality. 4.5. Betti numbers --
Ch. 5. Intersection theory. 5.1. Chow groups. 5.2. Cohomology of nonsingular toric varieties. 5.3. Riemann-Roch theorem. 5.4. Mixed volumes. 5.5. Bezout theorem. 5.6. Stanley's theorem.
Series Title: Annals of mathematics studies, no. 131.; William H. Roever lectures in geometry.
Responsibility: by William Fulton.
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