Back to Algebraic Geometry Seminar: Spring 2015
Algebraic Geometry Seminar
Date: Tuesday, Apr 7, 2015
Time: 3:30PM - 4:30PM
Location: LCB 215
Nikolaos Tziolas
University of Cyprus / Princeton
Title |
Automorphisms of smooth canonically polarised surfaces in positive characteristic. |
Abstract |
Let X be a smooth canonically polarised surface defined over an algebraically closed field of characteristic p>0. In this talk I will present some results about the geometry of X in the case when the automorphism scheme 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. |
Algebraic Geometry