Decompositions of ideals of minors meeting a submatrix

Abstract

We compute the primary decomposition of certain ideals generated by subsets of minors in a generic matrix or in a generic symmetric matrix, or subsets of Pfaffians in a generic skew-symmetric matrix. Specifically, the ideals we consider are generated by minors that have at least some given number of rows and columns in certain submatrices.

10 pages. v2: minor corrections. v3: minor changes, final version to appear in Comm. Alg