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arXiv · 2409.05705

Set-Theoretically Perfect Ideals and Residual Intersections

S. Hamid Hassanzadeh
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Abstract

This paper studies algebraic residual intersections in rings with Serre's condition \( S_{s} \). 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.

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S. Hamid Hassanzadeh. 2024-09-09. Set-Theoretically Perfect Ideals and Residual Intersections. https://arxiv.org/abs/2409.05705

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