Linquan Ma : F-injectivity and Buchsbaum singularities

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Oct. 2, 2013, 4 p.m.

In

SEO 427

Abstract

Let $(R,\mathfrak{m})$ be a local ring of positive characteristic. We show that when $H_{\mathfrak{m}}^i(R)$ has finite length for all $i<\dim R$, $R$ is F-injective if and only if every ideal generated by a system of parameters is Frobenius closed. As a corollary, we answer a question of Takagi that F-injective singularities with isolated non-Cohen-Macaulay locus are Buchsbaum. Some partial results in characteristic 0 for Du Bois singularities will also be discussed.