European Journal of Mathematics

, Volume 4, Issue 2, pp 439–524 | Cite as

Euler characteristics of Hilbert schemes of points on simple surface singularities

  • Ádám GyengeEmail author
  • András Némethi
  • Balázs Szendrői
Research Article


We study the geometry and topology of Hilbert schemes of points on the orbifold surface Open image in new window , respectively the singular quotient surface Open image in new window , where Open image in new window 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.


Hilbert scheme Singularities Euler characteristic Generating series Young wall 

Mathematics Subject Classification

14N10 05E10 



The authors would like to thank Gwyn Bellamy, Alastair Craw, Eugene Gorsky, Ian Grojnowski, Kevin McGerty, Iain Gordon, Tomas Nevins and Tamás Szamuely for helpful comments and discussions.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUK

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