Equivariant K-Theory Classes of Matrix Orbit Closures
Equivariant K-Theory Classes of Matrix Orbit Closures
复制标题
矩阵轨道闭包的等变K理论类
DOI：
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发表时间：
2019
影响因子：
1
通讯作者：
Alex Fink
中科院分区：
文献类型：
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作者：
A. Berget;Alex Fink
群 $G = extrm{GL}_r(k) imes (k^ imes )^n$ 作用于 $extbf{A}^{ri imes n}$，即 $r$×$n$ 矩阵的空间：$ extrm{GL}_r(k)$ 通过行运算起作用，$(k^ imes )^n$ 缩放列。矩阵轨道闭合是针对该动作的点轨道的 Zariski 闭合。我们证明$extbf{A}^{rimes n}$的$G$-等变$K$-理论中这种轨道闭合的类是由泛点的拟阵确定的。我们为此类提供两个公式。证明的关键是证明矩阵轨道闭包具有有理奇点。
The group $G = extrm{GL}_r(k) imes (k^ imes )^n$ acts on $ extbf{A}^{r imes n}$, the space of $r$-by-$n$ matrices: $ extrm{GL}_r(k)$ acts by row operations and $(k^ imes )^n$ scales columns. A matrix orbit closure is the Zariski closure of a point orbit for this action. We prove that the class of such an orbit closure in $G$-equivariant $K$-theory of $ extbf{A}^{r imes n}$ is determined by the matroid of a generic point. We present two formulas for this class. The key to the proof is to show that matrix orbit closures have rational singularities.