Geometric Representation Theory Seminar
Monday, December 10, 2018 at 5:30pm to 6:30pm
Dori Bejleri (MIT)
Motivic Hilbert zeta functions of curves
The Grothendieck ring of varieties is the target of a rich invariant associated to any algebraic variety which witnesses the interplay between geometric, topological and arithmetic properties of the variety. The motivic Hilbert zeta function is the generating series for classes in this ring associated to a certain compactification of the unordered configuration space, the Hilbert scheme of points, of a variety. In this talk I will discuss the behavior of the motivic Hilbert zeta function of a reduced curve with arbitrary singularities. For planar singularities, there is a large body of work detailing beautiful connections with enumerative geometry, representation theory and topology. I will discuss some possible extensions of this picture to non-planar curves.