Cox rings / Ivan Arzhantsev, Moscow State University [and three others].

By:

Arzhantsev, I. V. (Ivan Vladimirovich), 1972-

Material type: Text

TextLanguage: English Original language: Russian Series: Cambridge studies in advanced mathematics ; 144Publisher: New York, NY, USA : Cambridge University Press, 2015Description: viii, 530 pages : illustrations ; 24 cmContent type:

text

Media type:

unmediated

Carrier type:

volume

ISBN:

9781107024625 (hardback)
1107024625 (hardback)

Uniform titles:

Koltsa Koksa. English

Subject(s):

DDC classification:

516.3/53 23

LOC classification:

QA564 .A7913 2015

Other classification:

MAT038000

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"-- Provided by publisher.

Holdings ( 1 )
Title notes ( 2 )

Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
Book	Library	516-2015 (Browse shelf(Opens below))	Available		AT-ISTA#002651

Total holds: 0

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Previous	515-2025 An introduction to microlocal analysis /	516 Integral geometry and geometric probability	516 An Invitation to Algebraic Geometry (Universitext).	516 Cox rings /	516 Cartan for beginners : differential geometry via moving frames and exterior differential systems /	516-195x Geometric integration theory.	516-196x Foundations of Differential Geometry (Wiley Classics Library).	Next

Includes bibliographical references (pages 501-515) and 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"-- Provided by publisher.