Emelie Arvidsson: The singularities of the MMP in positive characteristic and applications to moduli of stable surfaces

Abstract:

My talk will be about the cohomological properties of the singularities that appear in the context of the Minimal Model Program. In particular, we will see that these singularities behave differently over the complex numbers and over an algebraically closed field of positive characteristic. I will discuss some consequences this pathological characteristic p behavior has, in particular when trying to formulate a moduli theory for varieties of general type in positive characteristics. In the end of my talk, we will focus on dimension three. We will see some positive results and discuss how these results can be applied to the moduli theory of stable surfaces in characteristic \(p>5\). This talk will be based on joint work with F. Bernasconi and Zs. Patakfalvi, as well as joint work with Q. Posva.