17 nov 2015 -- 14:30
Aula De Blasi, Dip. Matematica, Università "Tor Vergata", Roma
Abstract.
An important tool in studying open algebraic surfaces is the logarithmic Minimal Model Program. Although in dimension two its general mechanism is well understood, in concrete problems we need an analysis which goes far beyond the general framework. For log surfaces with reduced boundaries the usage of almost minimal models (due to Miyanishi, Fujita and others), which allows to avoid singularities, turned out to be very successful. Recently we generalized this approach to boundaries with coefficient 12 and used it in particular in the proof of the Coolidge-Nagata conjecture (2015, coauthored with M. Koras) concerning cuspidal planar curves. We will discuss a more general form of this approach showing how to apply it to other problems concerning surfaces of log general type.