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

Format:

Book

Author/Creator:

Fulton, William, author.

Series:

Annals of mathematics studies ; no. 131.

William H. Roever lectures in geometry.

Annals of Mathematics Studies ; 314

Language:

English

Subjects (All):

Toric varieties.

Physical Description:

1 online resource (171 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

In English.

System Details:

Mode of access: World Wide Web.

Summary:

Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are "ed without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.

Contents:

Frontmatter

Contents

Preface

Errata

Chapter 1. Definitions and examples

Chapter 2. Singularities and compactness

Chapter 3. Orbits, topology, and line bundles

Chapter 4. Moment maps and the tangent bundle

Chapter 5. Intersection theory

Notes

References

Index of Notation

Index

Notes:

Includes bibliographical references and indexes.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400882526

1400882524

OCLC:

979747116