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Cox rings

Arzhantsev, I. V. (1972-)

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Cox rings

Record Type:	Electronic resources : Monograph/item
Title/Author:	Cox rings/ Ivan Arzhantsev ... [et al.].
other author:	Arzhantsev, I. V.
Published:	Cambridge :Cambridge University Press, : 2015.,
Description:	viii, 530 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Algebraic varieties. -
Online resource:	https://doi.org/10.1017/CBO9781139175852
ISBN:	9781139175852

Cox rings
Kolʹtsa Koksa.English

Cox rings[electronic resource] /Ivan Arzhantsev ... [et al.]. - Cambridge :Cambridge University Press,2015. - viii, 530 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;144. - Cambridge studies in advanced mathematics ;144..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9781139175852Subjects--Topical Terms:

555734
Algebraic varieties.

LC Class. No.: QA564

Dewey Class. No.: 516.353

Cox rings
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130 1 0 $a Kolʹtsa Koksa. $l English $3 3470391
245 1 0 $a Cox rings $h [electronic resource] / $c Ivan Arzhantsev ... [et al.].
260 $a Cambridge : $b Cambridge University Press, $c 2015.
300 $a viii, 530 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 144
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
520 $a 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.
650 0 $a Algebraic varieties. $3 555734
650 0 $a Rings (Algebra) $3 540500
700 1 $a Arzhantsev, I. V. $q (Ivan Vladimirovich), $d 1972- $3 3470392
830 0 $a Cambridge studies in advanced mathematics ; $v 144. $3 3470393
856 4 0 $u https://doi.org/10.1017/CBO9781139175852