Euler characteristics of Hilbert schemes of points on simple surface singularities

Gyenge, Ádám and Némethi, András and Szendrői, Balázs (2018) Euler characteristics of Hilbert schemes of points on simple surface singularities. EUROPEAN JOURNAL OF MATHEMATICS, 4 (2). pp. 439-524. ISSN 2199-675X

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Abstract

We study the geometry and topology of Hilbert schemes of points on the orbifold surface [InlineEquation not available: see fulltext.], respectively the singular quotient surface [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.] is a finite subgroup 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. © 2018, Springer International Publishing AG, part of Springer Nature.

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