On the factoriality of Cox rings

被引:9
|
作者
Arzhantsev, I. V. [1 ]
机构
[1] Moscow MV Lomonosov State Univ, Moscow, Russia
关键词
total coordinate ring; Cox ring; algebraic variety; factorial ring; graded factoriality; divisor class group; torsion; Weil divisor; Cartier divisor; TOTAL COORDINATE RING; VARIETY;
D O I
10.1134/S0001434609050022
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The generalized Cox construction associates with an algebraic variety a remarkable invariant-its total coordinate ring, or Cox ring. In this note, we give a new proof of the factoriality of the Cox ring when the divisor class group of the variety is finitely generated and free. The proof is based on the notion of graded factoriality. We show that if the divisor class group has torsion, then the Cox ring is again factorially graded, but factoriality may be lost.
引用
收藏
页码:623 / 629
页数:7
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