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Transformation Groups

, Volume 23, Issue 3, pp 671–705 | Cite as

EQUIVARIANT HIRZEBRUCH CLASSES AND MOLIEN SERIES OF QUOTIENT SINGULARITIES

  • MARIA DONTEN-BURY
  • ANDRZEJ WEBER
Open Access
Article

Abstract

We study properties of the Hirzebruch class of quotient singularities ℂ n /G, where G is a finite matrix group. The main result states that the Hirzebruch class coincides with the Molien series of G under suitable substitution of variables. The Hirzebruch class of a crepant resolution can be described specializing the orbifold elliptic genus constructed by Borisov and Libgober. It is equal to the combination of Molien series of centralizers of elements of G. This is an incarnation of the McKay correspondence. The results are illustrated with several examples, in particular of 4-dimensional symplectic quotient singularities.

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WarsawWarszawaPoland
  2. 2.Institute of MathematicsFreie Universität BerlinBerlinGermany
  3. 3.Institute of Mathematics, Polish Academy of SciencesWarszawaPoland

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