2022/11/15 by Vaibhav Pandey, Pandey, Vaibhav, Yevgeniya Tarasova +1
Mathematics · #13A35 (Primary) 14M06 #13C40 #14M10 #14M12 (Secondary) #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2211.07922
openalex publication_date 2022/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.