Linkage and $F$-Regularity of Determinantal Rings

Vaibhav Pandey; Yevgeniya Tarasova

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arXiv · 2211.07922

Linkage and $F$-Regularity of Determinantal Rings

Vaibhav Pandey·Yevgeniya Tarasova

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Abstract

In this paper, we prove that the generic link of a generic determinantal ring defined by maximal minors is strongly $F$-regular. In the process, we strengthen a result of Chardin and Ulrich in the graded setting. They showed that the generic residual intersections of a complete intersection ring with rational singularities again have rational singularities. We show that if the said complete intersection is defined by homogeneous elements and is $F$-rational, then in fact, its generic residual intersections are strongly $F$-regular in positive prime characteristic. Hochster and Huneke showed that determinantal rings are strongly $F$-regular; however, their proof is quite involved. Our techniques allow us to give a new and simple proof of the strong $F$-regularity of determinantal rings defined by maximal minors.

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BibTeX RIS

Vaibhav Pandey, Yevgeniya Tarasova. 2024-02-17. Linkage and $F$-Regularity of Determinantal Rings. https://arxiv.org/abs/2211.07922

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