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Ideals of Adjacent Minors

Serkan Hosten·Seth Sullivant
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Abstract

We give a description of the minimal primes of the ideal generated by the 2 x 2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m x m minors of an m x n generic matrix when the characteristic of the ground field is zero. A key intermediate result is the proof that the ideals which appear as minimal primes are, in fact, prime ideals. This introduces a large new class of mixed determinantal ideals that are prime.

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Serkan Hosten, Seth Sullivant. 2003-06-23. Ideals of Adjacent Minors. https://arxiv.org/abs/math/0306318

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