Du Bois singularities were defined by DuBois and Steenbrink in the 80's, and are important as the class of singularities where some key ideas from Hodge theory can be carried out. Their definition is quite complicated, but Karl Schwede recently gave a simple characterization in terms of resolution of singularities. As an application, Schwede shows that that F-injective singularities are DuBois, placing them among the pantheon of singularities that have (or are conjectured to have) characteristic p analogs in the world of tight closure. As another application, in joint work with Kovacs and Schwede, we prove a conjecture of Kollar stating that log canonical singularities are DuBois, at least in the Cohen-Macaulay case.

Lecture #13409

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