Cox Rings

China Internet Development Report 2018: Blue Book of World Internet Conference Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces.\n\nThis 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. Additional ISBNs 1107024625, 1316146863, 9781107024625, 9781316146866Cox Rings 1st Edition is written by Ivan Arzhantsev; Ulrich Derenthal; J�rgen Hausen; Antonio Laface and published by Cambridge University Press. ISBNs for Cox Rings are 9781316146866, 1316146863 and the print ISBNs are 9781107024625, 1107024625. Additional ISBNs include 1107024625, 1316146863, 9781107024625, 9781316146866.