Generating Series of the Poincaré Polynomials of Quasihomogeneous Hilbert Schemes

  • A. Buryak
  • B. L. Feigin
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 40)


In this paper we prove that the generating series of the Poincaré polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the numbers of quasihomogeneous components in a moduli space of sheaves on the projective plane. The answer is given in terms of characters of the affine Lie algebra \(\widehat{\mathit{sl}}_{m}\).


Modulus Space Irreducible Component Young Diagram Betti Number Power Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors are grateful to S.M. Gusein-Zade, M. Finkelberg and S. Shadrin for useful discussions.

A.B. is partially supported by a Vidi grant of the Netherlands Organization of Scientific Research, by the grants RFBR-10-01-00678, NSh-4850.2012.1 and the Moebius Contest Foundation for Young Scientists. Research of B.F. is partially supported by RFBR initiative interdisciplinary project grant 09-02-12446-ofi-m, by RFBR-CNRS grant 09-02-93106, RFBR grants 08-01-00720-a, NSh-3472.2008.2 and 07-01-92214-CNRSL-a.


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of MathematicsMoscow State UniversityMoscowRussia
  3. 3.National Research University Higher School of EconomicsMoscowRussia
  4. 4.Landau Institute for Theoretical PhysicsChernogolovkaRussia
  5. 5.Independent University of MoscowMoscowRussia

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