Cox Rings: 144 (Cambridge Studies in Advanced Mathematics, Series Number 144)
Cambridge University Press, 8/29/2014
EAN 9781107024625, ISBN10: 1107024625
Hardcover, 472 pages, 23.6 x 15.7 x 3.3 cm
Language: English
Originally published in English
Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous presentation of the basic concepts, other central topics include the case of finitely generated Cox rings and its relation to toric geometry; various classes of varieties with group actions; the surface case; and applications in arithmetic problems, in particular Manin's conjecture. The introductory chapters require only basic knowledge in algebraic geometry. The more advanced chapters also touch on algebraic groups, surface theory, and arithmetic geometry. Each chapter ends with exercises and problems. These comprise mini-tutorials and examples complementing the text, guided exercises for topics not discussed in the text, and, finally, several open problems of varying difficulty.
Introduction
1. Basic concepts
2. Toric varieties and Gale duality
3. Cox rings and combinatorics
4. Selected topics
5. Surfaces
6. Arithmetic applications.