论文标题
Git堆栈商的Kleiman标准
A Kleiman criterion for GIT stack quotients
论文作者
论文摘要
Kleiman的标准指出，对于$ x $，一个投影方案，除了它与曲线圆锥的关闭的每个非零元素成对时，只有当它与曲线圆锥的每个非零元素成对时，只有$ d $。换句话说，$ n^1（x）$中充分的除数锥是Nef锥的内部。在本文中，我们提出了一个类似的声明，该声明是由还原组$ g $执行的品种$ x $，并选择了$ g $ linearization $ l \ l \ to x $。在这种新的情况下，$ x $的丰富锥由g-ample锥体的GIT分解的单元代替，$ x $中的曲线被准单品替换为$ [x/g] $。
Kleiman's criterion states that, for $X$ a projective scheme, a divisor $D$ is ample if and only if it pairs positively with every non-zero element of the closure of the cone of curves. In other words, the cone of ample divisors in $N^1(X)$ is the interior of the nef cone. In this paper we present an analogous statement for a variety $X$ acted on by a reductive group $G$ with a choice of $G$-linearization $L \to X$. In this new context, the ample cone of $X$ is replaced by a cell in the variation of GIT decomposition of the G-ample cone, and curves in $X$ are replaced by quasimaps to $[X/G]$.
