Set-Theoretically Perfect Ideals and Residual Intersections
Commutative Algebra
2025-02-13 v2
Abstract
This paper studies algebraic residual intersections in rings with Serre's condition . It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a uniform upper bound for the multiplicity of residual intersections. In positive characteristic, it follows that residual intersections are cohomologically complete intersection and, hence, their variety is connected in codimension one.
Cite
@article{arxiv.2409.05705,
title = {Set-Theoretically Perfect Ideals and Residual Intersections},
author = {S. Hamid Hassanzadeh},
journal= {arXiv preprint arXiv:2409.05705},
year = {2025}
}
Comments
28 pages, the previous title "A free Approach to Residual Intersections " changed to "Set-Theoretically Perfect Ideals and Residual Intersections", to appear in J. London Math. Soc