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Mosc. Math. J., 2012, Volume 12, Number 1, Pages 21–36 (Mi mmj445)  

This article is cited in 3 scientific papers (total in 3 papers)

The classes of the quasihomogeneous Hilbert schemes of points on the plane

A. Buryakab

a Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Department of Mathematics, University of Amsterdam, Amsterdam, The Netherlands

Abstract: In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of $(1,k)$-quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric interpretation of the $q,t$-Catalan numbers. Finally, we investigate a connection between $(1,k)$-quasi-homogeneous Hilbert schemes and homogeneous nested Hilbert schemes.

Key words and phrases: Hilbert scheme, torus action, $q,t$-Catalan numbers.

DOI: https://doi.org/10.17323/1609-4514-2012-12-1-21-36

Full text: http://www.ams.org/.../abst12-1-2012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 14C05, 05A17
Received: November 18, 2010
Language:

Citation: A. Buryak, “The classes of the quasihomogeneous Hilbert schemes of points on the plane”, Mosc. Math. J., 12:1 (2012), 21–36

Citation in format AMSBIB
\Bibitem{Bur12}
\by A.~Buryak
\paper The classes of the quasihomogeneous Hilbert schemes of points on the plane
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 1
\pages 21--36
\mathnet{http://mi.mathnet.ru/mmj445}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-1-21-36}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2952423}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309364900002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Buryak, “The Moduli Space of Sheaves and a Generalization of MacMahon's Formula”, Funct. Anal. Appl., 47:2 (2013), 96–103  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Lee K., Li L., Loehr N.A., “Limits of Modified Higher Q, T-Catalan Numbers”, Electron. J. Comb., 20:3 (2013), P4  mathscinet  zmath  isi  elib
    3. Buryak A., Feigin B.L., Nakajima H., “a Simple Proof of the Formula For the Betti Numbers of the Quasihomogeneous Hilbert Schemes”, Int. Math. Res. Notices, 2015, no. 13, 4708–4715  crossref  mathscinet  zmath  isi  elib  scopus
  • Moscow Mathematical Journal
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