publication . Preprint . 2016

Hilbert schemes of points on some classes surface singularities

Gyenge, Ádám;
Open Access English
  • Published: 29 Sep 2016
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...
free text keywords: Mathematics - Algebraic Geometry, Mathematics - Combinatorics, Mathematics - Representation Theory
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