30/11, UFF. Campus do Gragoatá, Bloco H, sala 407.
10:3011:30 
Jean Vallès (Universitá de Pau et de Pays de L'adour),
Logarithmic bundles and line arrangements, an approach via the standard construction
Resumo. We propose an approach to study logarithmic sheaves associated with hyperplane arrangements on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on free line arrangements, recovering, thanks to this new approach, many known results and improving some of them about the socalled Terao's conjecture.
 12:0013:00 
Giancarlo Urzúa (PUC Chile),
On explicit boundedness for surfaces
Resumo. Kollár and ShepherdBarron (1988) introduced a natural compactification to the Gieseker moduli space of surfaces of general type with fixed invariants K^{2} and χ, which is analogous to the DeligneMumford (1969) compactification of the moduli space of curves of genus g>1. This compactification is coarsely represented by a projective scheme (due to Kollár 1990) because of Alexeev's proof of boundedness (1994). Surfaces parametrized by this moduli space are called (KSBA) stable surfaces. They admit at most slc singularities, and they may or may not be degenerations of canonical projective surfaces of general type (i.e. at most ADE singularities and K ample). Since this KSBA moduli space is represented by a projective scheme, we have a finite list of slc singularities in the stable surfaces which it parametrizes. It is a hard problem to write down that list.
In this talk, I will show effective bounds for a particular but relevant class of singularities (Tsingularities) in stable surfaces W with fixed K^{2}. When W is not rational, we can classify surfaces attaining the bound. When W is rational we can show where the problem is (to find optimal bounds). This is a joint work with Julie Rana. Similar bounds were found by Jonny Evans and Ivan Smith via symplectic topology, which can be seen as an obstruction to embed symplectically a rational homology ball B_{p,q} in a canonically polarized surface. At the end, I will show that noncanonically embedded B_{p,q}'s are unbounded in surfaces of general type, so the condition in EvansSmith was necessary, by means of the explicit stable 3dimensional MMP for Tdegenerations (joint with Paul Hacking and Jenia Tevelev). This last result is joint with Jonny Evans.

