Minimal resolution of A_k singularities as moduli spaces of Z/(k+1)Z-constellations

Abstract: It is a classical result that, for any finite subgroup G of SL(n,C), for n=2,3, there exists (at least) one crepant resolution of the singularity "affine n-space modulo G-action". When G is abelian, thanks to a work of Craw and Ishii, any such resolution can be interpreted as the fine moduli space of certain coherent sheaves, called G-constellations, which are stable with respect to a GIT stability condition. In my talk I will introduce the above mentioned notions and I will talk about some combinatorial objects that I have introduced to describe the two-dimensional setting. If time permits, I will also explain some three-dimensional phenomena.

Portuguesecommutative algebraalgebraic geometryanalysis of PDEsalgebraic topologydifferential geometryfunctional analysisgeneral topologygeometric topologyprobabilityrings and algebras

Audience: general audience

Seminários de Matemática da UFPB