23 may 2017 -- 14:30
sala Tricerri, DiMaI, Firenze
Abstract.
In this talk I will discuss the moduli of canonically polarized surfaces defined over an algebraically closed field of characteristic $p>0$ and the pathologies that appear compared to the characteristic zero case. In particular, unlike the characteristic zero case, there does not always exists a modular family. A modular family is a family with the property that up to etale base change, every other family is obtained from it by base change. I will explain the relation between this pathology and the existence of canonically polarized surfaces with nontrivial global vector fields, or equivalently with nonreduced automorphism scheme. Moreover, several results regarding the geometry of such surfaces will be presented.