Algebraic and Arithmetic Geometry Seminar

Canonical liftings and log structures

by Piotr Achinger (Instytut Matematyczny PAN)

Aula Magna (Dipartimento di Matematica)

Aula Magna

Dipartimento di Matematica


In the context of mirror symmetry, the moduli space of complex Calabi-Yau varieties acquires canonical local coordinates near a "large complex structure limit point". In characteristic p geometry, the formal deformation space of an ordinary Calabi-Yau variety tends to have such canonical coordinates ("Serre-Tate parameters") as well. As observed e.g. by Jan Stienstra, these situations are formally very similar, and one would like to compare the two when both make sense. A framework for doing this could be supplied by a version of Serre-Tate theory for log Calabi-Yau varieties. In my talk, I will describe the first step in this direction; a construction of canonical liftings modulo $p^2$ of certain log schemes. I will link this to a question of Keel describing global moduli of maximal log Calabi-Yau pairs.