Singularities of generic linkage via Frobenius powers

TL;DR

This paper investigates the relationship between F-pure thresholds of an ideal and its generic linkage over complex polynomial rings, establishing bounds and connections to log canonical thresholds.

Contribution

It proves a uniform bound on the difference of F-pure thresholds via Frobenius powers, linking these invariants to generic linkage.

Findings

Bound on the difference between F-pure thresholds of linked ideals

Evidence that the F-pure threshold of an ideal is less than that of its linkage

Recovery of a known result on log canonical thresholds by Niu

Abstract

Let $I$ be an equidimensional ideal of a ring polynomial $R$ over $\mathbb{C}$ and let $J$ be its generic linkage. We prove that there is a uniform bound of the difference between the F-pure thresholds of $I_p$ and $J_p$ via the generalized Frobenius powers of ideals. This provides evidence that the F-pure threshold of an equidimensional ideal $I$ is less than that of its generic linkage. As a corollary we recover a result on log canonical thresholds of generic linkage by Niu.