Automorphisms of smooth canonically polarised surfaces in characteristic 2

Topology of Algebraic Varieties
Topic:Automorphisms of smooth canonically polarised surfaces in characteristic 2
Speaker:Nikolaos Tziolas
Affiliation:University of Cyprus
Date:Wednesday, February 25
Time/Room:11:15am - 12:15pm/S-101
Video Link:http://video.ias.edu/tav/2015/0225-NikolaosTziolas

Let $X$ be a smooth canonically polarised surface defined over an algebraically closed field of characteristic 2. In this talk I will present some results about the geometry of $X$ in the case when the automorphism scheme $\mathrm{Aut}(X)$ of $X$ is not smooth, or equivalently $X$ has nontrivial global vector fields. This is a situation that appears only in positive characteristic and is intimately related to the structure of the moduli stack of canonically polarised surfaces in positive characteristic because the smoothness of the automorphism scheme is the obstruction for the moduli stack to be Deligne-Mumford, something that is always true in characteristic zero but not in general in positive characteristic. One of the results that will be presented in this talk is that smooth canonically polarised surfaces with non smooth automorphism scheme and "small" invariants are algebraically simply connected and uniruled.