$F$-singularities under generic linkage

Abstract

Let $R=k[x_1,\dots ,x_n]$ 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 $S=R[u_{ij}{]}_{c\times r}$. 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 $(S,J)$.

11 pages, final version

References in corpus (1)

• A survey of test ideals