Generators of Residual Intersections

TL;DR

This paper provides a description of generators for residual intersections of ideals, linking them to lower residual intersections and links under certain technical conditions, advancing understanding in ideal theory.

Contribution

It introduces a new description of generators of residual intersections in terms of lower residuals and links, under specific assumptions.

Findings

Generators of residual intersections can be expressed via lower residual intersections.

Residual intersections can be linked to each other under certain deviation conditions.

Provides a framework for understanding residual intersections in algebraic geometry.

Abstract

Under suitable technical assumptions, a description is given for the generators of $s$-residual intersections of an ideal $I$ in terms of lower residual intersections, if $s \geq \mu(I)-2$. This implies that $s$-residual intersections can be expressed in terms of links, if the deviation of $I$ is less than or equal to 3 and some other hypotheses are satisfied.