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arXiv · 1503.05799

Principal Minor Ideals and Rank Restrictions on their Vanishing Sets

Ashley K. Wheeler
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Abstract

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 $n\times n$ rank $n-2$ matrices whose size $n-2$ principal minors vanish; this set has dimension $n^2-n-4$.

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BibTeXRIS

Ashley K. Wheeler. 2015-08-03. Principal Minor Ideals and Rank Restrictions on their Vanishing Sets. https://doi.org/10.1016/j.jalgebra.2016.08.013

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