Description
Abstract:
We generalize Artin-Verdier, Esnault and Wunram construction of McKay correspondence toarbitrary Gorenstein surface singularities. The key idea is the definition and a systematic use of a degeneracymodule, which is an enhancement of the first Chern class construction via a degeneracy locus. We study also de-formation and moduli questions. Among our main result we quote: a full classification of special reflexive MCMmodules on normal Gorenstein surface singularities in terms of divisorial valuations centered at the singularity,a first Chern class determination at an adequate resolution of singularities, construction of moduli spaces ofspecial reflexive modules, a complete classification of Gorenstein normal surface singularities in representationtypes, and a study on the deformation theory of MCM modules and its interaction with their pullbacks atresolutions. As a consequence of the theory we confirm a conjecture of Drodz, Greuel and Kashuba in theGorenstein case. Joint work with Agustin Romano.
For Zoom access please contact Andras Stipsicz (stipsicz.andras[a]renyi.hu).