Deformations of log canonical singularities
arXiv:1803.03325
Abstract
We prove that the cohomology sheaves of the relative dualizing complex of a flat family of varieties with semi-log-canonical or Du Bois singularities are flat and commute with base change. This is a local version of our earlier similar result where the family was assumed to be projective. We also derive several consequences for deformations of semi-log-canonical and of Du Bois singularities.
The results of this paper are now contained in a new, substantially expanded version entitled "Deformations of log canonical and F-pure singularities"