Algebraic Geometry Seminar
Linquan Ma
University of Michigan
F-injectivity and Buchsbaum singularities
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.
Wednesday October 2, 2013 at 4:00 PM in SEO 427