Elsevier

Journal of Algebra

Volume 277, Issue 2, 15 July 2004, Pages 615-642
Journal of Algebra

Ideals of adjacent minors

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Abstract

We give a description of the minimal primes of the ideal generated by the 2×2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m×m minors of an m×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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Partially supported by the National Science Foundation (DMS-0200729).