Cox Rings (Cambridge Studies in Advanced Mathematics) by Arzhantsev, Ivan

Description: 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.

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EAN: 9781107024625

UPC: 9781107024625

ISBN: 9781107024625

MPN: N/A

Number of Pages: 472 Pages

Publication Name: Cox Rings

Language: English

Publisher: Cambridge University Press

Item Height: 1.3 in

Publication Year: 2014

Subject: Topology, Algebra / General, Geometry / Algebraic

Item Weight: 30 Oz

Type: Textbook

Author: Antonio Laface, Jürgen Hausen, Ivan Arzhantsev, Ulrich Derenthal

Item Length: 9.3 in

Subject Area: Mathematics

Series: Cambridge Studies in Advanced Mathematics Ser.

Item Width: 6.2 in

Format: Hardcover