论文标题
换向器矩阵定义的代数集
Algebraic sets defined by the commutator matrix
论文作者
论文摘要
在本文中，我们研究了代数对矩阵的成对组，这些矩阵的对角线的对角线消失了，或者其抗双向对角线的对角线。我们找到了这两组的坐标环及其交点的参数系统，并表明它们是完整的交叉点。此外，我们证明，这些代数集在正面的主要特征上是$ f $ pure，并且代数矩阵的代数矩阵与零对角换向器的矩阵为$ f $ rogular。
In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find a system of parameters for the coordinate rings of these two sets and their intersection and show that they are complete intersections. Moreover, we prove that these algebraic sets are $F$-pure over a field of positive prime characteristic and the algebraic set of pairs of matrices with the zero diagonal commutator is $F$-regular.
