Linkage and $F$-Regularity of Determinantal Rings
Abstract
In this paper, we prove that the generic link of a generic determinantal ring defined by maximal minors is strongly -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 -rational, then in fact, its generic residual intersections are strongly -regular in positive prime characteristic. Hochster and Huneke showed that determinantal rings are strongly -regular; however, their proof is quite involved. Our techniques allow us to give a new and simple proof of the strong -regularity of determinantal rings defined by maximal minors.
Keywords
Cite
@article{arxiv.2211.07922,
title = {Linkage and $F$-Regularity of Determinantal Rings},
author = {Vaibhav Pandey and Yevgeniya Tarasova},
journal= {arXiv preprint arXiv:2211.07922},
year = {2024}
}
Comments
Minor changes and more details added to the statement and proof of Theorem 5.7; corresponding changes in the introduction. Final version. To appear in IMRN