Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Cox rings / Ivan Arzhantsev...[et al.].

By: Contributor(s): Material type: TextTextSeries: Cambridge studies in advanced mathematics ; 144Publication details: New York : Cambridge University Press, 2015.Description: viii, 530 p. : illustrations ; 24 cmISBN:
  • 9781107024625 (hardback)
Subject(s): DDC classification:
  • 516.353 23 Ar797
Contents:
Introduction; 1. Basic concepts; 2. Toric varieties and Gale duality; 3. Cox rings and combinatorics; 4. Selected topics; 5. Surfaces; 6. Arithmetic applications; Bibliography-- Index.
Summary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.

Includes bibliographical references (pages 501-515) and index.

Introduction;
1. Basic concepts;
2. Toric varieties and Gale duality;
3. Cox rings and combinatorics;
4. Selected topics;
5. Surfaces;
6. Arithmetic applications;
Bibliography--
Index.

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.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in