On Cox rings of K3 surfaces

被引：34

作者：

Artebani, Michela ^{[1
]}

Hausen, Juergen ^{[2
]}

Laface, Antonio ^{[1
]}

机构：

[1] Univ Concepcion, Dept Matemat, Concepcion, Chile

[2] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany

来源：

COMPOSITIO MATHEMATICA | 2010年 / 146卷 / 04期

关键词：

Cox rings; K3; surfaces; K-3; SURFACES; COMBINATORICS;

D O I：

10.1112/S0010437X09004576

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Cox rings of K3 surfaces. A first result is that a K3 surface has a finitely generated Cox ring if and only if its effective cone is rational polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3 surfaces of Picard number two, and explicitly compute the Cox rings of generic K3 surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.

引用

页码：964 / 998

页数：35

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