Principal minor ideals and rank restrictions on their vanishing sets

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Principal minor ideals and rank restrictions on their vanishing sets

Wheeler, Ashley K.

Journal of algebra, 01/2017, Volume: 469

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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×n rank n−2 matrices whose size n−2 principal minors vanish; this set has dimension n2−n−4.

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Wheeler, Ashley K.

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