Mattia Talpo (Simon Fraser University)
A logarithmic McKay correspondence and derived invariance for parabolic sheaves
|Tue, Apr 24, 2018, 13:15 - 14:45
Seminar Room A
In this talk I will explain some joint work with Sarah Scherotzke and Nicolò Sibilla, where we prove a "limit" version of the derived McKay correspondence in the context of logarithmic geometry. The two sides of the derived equivalence in our case are given by objects called the "infinite root stack" and the "valuativization", that correspond to different ways of enhancing the central fiber of some simple kind of degenerations. Our result also implies the rather surprising fact that the derived category of parabolic sheaves on a variety with a normal crossings divisor is invariant under certain blowups. Along the way I will review some basics about the objects involved, and try to highlight their relevance to a modern approach to curve and sheaf-counting theories for singular varieties.