Euler characteristics of Hilbert schemes of points on simple surface singularities

Ádám Gyenge; András Némethi; Balázs Szendrői

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arXiv · 1512.06848

Euler characteristics of Hilbert schemes of points on simple surface singularities

Ádám Gyenge·András Némethi·Balázs Szendrői

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Abstract

We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in terms of an explicit formula involving a specialized character of the basic representation of the corresponding affine Lie algebra; we conjecture that the same result holds also in type E. Our results are consistent with known results in type A, and are new for type D.

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BibTeX RIS

Ádám Gyenge, András Némethi, Balázs Szendrői. 2018-02-01. Euler characteristics of Hilbert schemes of points on simple surface singularities. https://arxiv.org/abs/1512.06848

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