F-singularities under generic linkage

2016/07/14 by Linquan Ma, Ma, Linquan, Janet Page +7
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.1607.03972

11 pages, final version

arxiv created 2018/03/18 · arxiv updated 2018/03/20

Abstract

Let R=k[x₁,…,x_n] be a polynomial ring over a prefect field of positive characteristic. Let I be an unmixed ideal in R and let J be a generic link of I in S=R[u_ij]_{c × r}. We describe the parameter test submodule of S/J in terms of the test ideal of the pair (R, I) when a reduction of I is a complete intersection or almost complete intersection. As an application, we deduce a criterion for when S/J has F-rational singularities in these cases. We also compare the F-pure threshold of (R, I) and (S, J).

Related

• Singularities of generic linkage via Frobenius powers
• F-purity and the F-pure threshold as invariants of linkage
• Singularities of generic linkage of algebraic varieties
• Linkage and F-Regularity of Determinantal Rings
• Lower Bounds on the F-pure Threshold and Extremal Singularities