Algebraic sets defined by the commutator matrix
Commutative Algebra
2020-06-25 v1
Abstract
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 -pure over a field of positive prime characteristic and the algebraic set of pairs of matrices with the zero diagonal commutator is -regular.
Cite
@article{arxiv.2006.13514,
title = {Algebraic sets defined by the commutator matrix},
author = {Zhibek Kadyrsizova and Madi Yerlanov},
journal= {arXiv preprint arXiv:2006.13514},
year = {2020}
}