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arXiv · 1607.03972

$F$-singularities under generic linkage

Linquan Ma·Janet Page·Rebecca R. G.·William Taylor·Wenliang Zhang
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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 $(S, J)$.

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Linquan Ma, Janet Page, Rebecca R. G., William Taylor, Wenliang Zhang. 2016-07-14. $F$-singularities under generic linkage. https://arxiv.org/abs/1607.03972

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