English

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 Ss S_{s} . 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.

Keywords

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

R2 v1 2026-06-28T18:38:39.463Z