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Young Walls and Equivariant Hilbert Schemes of Points in Type D

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Singularities and Their Interaction with Geometry and Low Dimensional Topology

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Abstract

We give a combinatorial proof for a multivariable formula of the generating series of type D Young walls. Based on this we give a motivic refinement of a formula for the generating series of Euler characteristics of Hilbert schemes of points on the orbifold surface of type D.

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Notes

  1. 1.

    In [13, 14], these arrangements are called proper Young walls. Since we will not meet any other Young wall, we will drop the adjective proper for brevity.

  2. 2.

    This is the properness condition of [13].

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Acknowledgements

The author is thankful to Jim Bryan, András Némethi and Balázs Szendrői for fruitful conversations about the topic. The author was supported by the EPSRC grant EP/R045038/1 while completing this work.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, UK

    Ádám Gyenge

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  1. Ádám Gyenge
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Correspondence to Ádám Gyenge .

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Editors and Affiliations

  1. Basque Center for Applied Mathematics Ikerbasque (Basque Foundation for Science), Bilbao, Spain

    Javier Fernández de Bobadilla

  2. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

    Tamás László

  3. Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    András Stipsicz

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Gyenge, Á. (2021). Young Walls and Equivariant Hilbert Schemes of Points in Type D . In: Fernández de Bobadilla, J., László, T., Stipsicz, A. (eds) Singularities and Their Interaction with Geometry and Low Dimensional Topology . Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-61958-9_3

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