论文标题
代数堆栈的Cox环
Cox rings of algebraic stacks
论文作者
论文摘要
我们给出了以下环的乘法结构的正确定义：一般代数堆栈上可逆滑轮的Cox环；等级的Cox环在正常和出色的代数堆栈上。我们表明，这种Cox环始终存在，并根据扩展组建立了（非）独特性。此外，我们将我们的定义与各种Cox环的经典结构进行了比较。最后，我们对莫里梦想堆栈的理论提出了应用。
We give a proper definition of the multiplicative structure of the following rings: the Cox ring of invertible sheaves on a general algebraic stack; and the Cox ring of rank one reflexive sheaves on a normal and excellent algebraic stack. We show that such Cox rings always exist and establish their (non-)uniqueness in terms of an Ext-group. Moreover, we compare our definition with the classical construction of a Cox ring on a variety. Finally, we give an application to the theory of Mori dream stacks.
