Decompositions of ideals of minors meeting a submatrix

TL;DR

This paper computes the primary decomposition of ideals generated by minors meeting specific submatrix criteria in generic, symmetric, or skew-symmetric matrices, advancing understanding of their algebraic structure.

Contribution

It provides explicit primary decompositions for ideals generated by minors with specified submatrix conditions in various matrix types, a novel algebraic insight.

Findings

Primary decompositions for ideals of minors meeting submatrix conditions

Explicit descriptions for ideals in generic, symmetric, and skew-symmetric matrices

Enhanced understanding of algebraic structure of these ideals

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.