Christian Liedtke:
Serre-Tate lifts for Calabi-Yau varieties
Time and place
Friday, 28.10.11, 10:00-11:00, Raum 404, Eckerstr. 1
Abstract
For an ordinary Abelian variety over a perfect field of\npositive characteristic, Serre and Tate discovered a\ncanonical lift over the Witt ring. Later, this has been\ngeneralized to varieties with trivial tangent bundles by\nNori and Srinivas. In this talk, we will construct a\ncanonical lift for ordinary varieties with trivial\ncanonical sheaves, which generalizes Serre-Tate as well as\nNori-Srinivas. As applications, we obtain a Serre-Tate\ntheory for Calabi-Yau varieties (as anticipated by\nStienstra), as well as a Bogomolov-Tian-Todorov\nunobstructedness theorem for such varieties (building on\nwork of Ekedahl and Shepherd-Barron). We also discuss\nexamples due to Hirokado, Schroeer, Schoen, Cynk and van\nStraten of non-liftable Calabi-Yau varieties for which\nunobstructedness of deformations fails.\n