Zsolt Patakfalvi:
Base change for the relative canonical sheaf in families of normal varieties
Zeit und Ort
Freitag, 17.12.10, 11:15-12:15, Raum 127, Eckerstr. 1
Zusammenfassung
In higher dimensional algebraic geometry one of the most important invariant\nof a variety is the canonical morphism, i.e., the morphism determined by\nsome high enough reflexive power of the canonical sheaf. For this reason, in\nhigher dimensional moduli theory, it is crucial to understand the base\nchange behavior of the relative canonical sheaf, and of its reflexive\npowers. This talk will focus on the base change behavior of the relative\ncanonical sheaf itself. It has been known for a while that it is compatible\nwith base change if the fibers are Cohen-Macaulay. Recently, compatibility\nhas been proven if the fibers are Du Bois. I will present a statement\nthat underscores the importance of these results by showing that this\ncompatibility does not hold generally in families of normal varieties, not\neven over smooth bases.