Singularities of generic linkage via Frobenius powers

2022/07/13 by Jiamin Li, Li, Jiamin
Computer Science · Mathematics · #14B05 13A35 #Advanced Differential Equations and Dynamical Systems #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2207.06380

openalex publication_date 2022/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I be an equidimensional ideal of a ring polynomial R over 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.

Related

• F-singularities under generic linkage
• F-purity and the F-pure threshold as invariants of linkage
• Frobenius powers
• F-thresholds, tight closure, integral closure, and multiplicity bounds
• On the existence of F-thresholds and related limits