Fulton Introduction to Toric Varieties. (AM-131), Volume 131

1. Auflage 2016
ISBN: 978-1-4008-8252-6
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 131, 180 Seiten

Reihe: Annals of Mathematics Studies

No detailed description available for "Introduction to Toric Varieties. (AM-131), Volume 131".

Autoren/Hrsg.

Fulton, William

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Ch. 1 Definitions and examples

1.1 Introduction 3

1.2 Convex polyhedral cones 8

1.3 Affine toric varieties 15

1.4 Fans and toric varieties 20

1.5 Toric varieties from polytopes 23

Ch. 2 Singularities and compactness

2.1 Local properties of toric varieties 28

2.2 Surfaces; quotient singularities 31

2.3 One-parameter subgroups; limit points 36

2.4 Compactness and properness 39

2.5 Nonsingular surfaces 42

2.6 Resolution of singularities 45

Ch. 3 Orbits, topology, and line bundles

3.1 Orbits 51

3.2 Fundamental groups and Euler characteristics 56

3.3 Divisors 60

3.4 Line bundles 63

3.5 Cohomology of line bundles 73

Ch. 4 Moment maps and the tangent bundle

4.1 The manifold with singular corners 78

4.2 Moment map 81

4.3 Differentials and the tangent bundle 85

4.4 Serre duality 87

4.5 Betti numbers 91

Ch. 5 Intersection theory

5.1 Chow groups 96

5.2 Cohomology of nonsingular toric varieties 101

5.3 Riemann-Roch theorem 108

5.4 Mixed volumes 114

5.5 Bezout theorem 121

5.6 Stanley's theorem 124

Notes 131

References 149

Index of Notation 151

Index 155

Über Autor(innen)

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