Local cohomology of Du Bois singularities and applications to families

Linquan Ma, Karl Schwede, Kazuma Shimomoto

In this paper we study the local cohomology modules of Du Bois singularities. Let $(R,m)$ be a local ring, we prove that if $R_{red}$ is Du Bois, then $H_m^i(R)\to H_m^i(R_{red})$…