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Euler characteristics of Hilbert schemes of simple surface singularities

Algebraic Geometry

Speaker: Adam Gyenge, University of British Columbia
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Location: 2112 MSB
Start time: Wed, Oct 18 2017, 11:00AM

Given a smooth surface, the generating series of Euler characteristics of its Hilbert schemes of points can be given in closed form by (a specialisation of) Goettsche's formula. I will discuss a generalisation of this formula to surfaces with rational double points. A certain representation of the affine Lie algebra corresponding to the surface singularity (via the McKay correspondence), and its crystal basis theory, play an important role in our approach. Joint work with András Némethi and Balázs Szendrői.