Generating Residual Intersections of Determinantal Ideals

TL;DR

This paper investigates the structure of residual intersections of determinantal ideals, revealing that for generic 2x n matrices, these intersections can be expressed as sums of linked ideals, advancing understanding in algebraic geometry.

Contribution

It demonstrates that n-residual intersections of determinantal ideals of generic 2x n matrices are sums of links, providing a new explicit description in this context.

Findings

Residual intersections of these ideals are sums of links.

Provides explicit descriptions for residual intersections of determinantal ideals.

Advances understanding of ideal linkage in algebraic geometry.

Abstract

If $I$ is a perfect ideal in a local Cohen-Macaulay ring, the generators of ideals linked to $I$ are well understood. However, the generators of the residual intersections of $I$ have only been computed in a few special cases. In this paper, we show that the $n$-residual intersections of determinantal ideals of generic $2\times n$ matrices are sums of links.