Principal minor ideals and rank restrictions on their vanishing sets

JOURNAL OF ALGEBRA

卷:469

Article

Wheeler, Ashley K.¹ 

[1] Univ Arkansas, Dept Math Sci, Fayetteville, AR 72701 USA

关键词: Principal minor ideals;    Determinantal ideals;    Matroid varieties;    Positroid varieties;    Grassmannians;   

DOI  :  10.1016/j.jalgebra.2016.08.013

来源: Elsevier

【 摘 要 】

All matrices we consider have entries in a fixed algebraically closed field K. A minor of a square matrix is principal means it is defined by the same row and column indices. We study the ideal generated by size t principal minors of a generic matrix, and restrict our attention to locally closed subsets of its vanishing set, given by matrices of a fixed rank. The main result is a computation of the dimension of the locally closed set of n x n rank n - 2 matrices whose size n - 2 principal minors vanish; this set has dimension n(2) - n - 4. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free