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On the power structure over the Grothendieck ring of varieties and its applications

Proceedings of the Steklov Institute of Mathematics volume 258, Article number: 53 (2007) Cite this article

Abstract

We discuss the notion of a power structure over a ring and the geometric description of the power structure over the Grothendieck ring of complex quasi-projective varieties and show some examples of applications to generating series of classes of configuration spaces (for example, nested Hilbert schemes of J. Cheah) and wreath product orbifolds.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

    S. M. Gusein-Zade

  2. Departamento de Álgebra, Universidad Complutense de Madrid, Plaza de Ciencias 3, Ciudad Universitaria, 28040, Madrid, Spain

    I. Luengo & A. Melle-Hernández

Authors
  1. S. M. Gusein-Zade
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  2. I. Luengo
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  3. A. Melle-Hernández
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Corresponding author

Correspondence to S. M. Gusein-Zade.

Additional information

To Vladimir Igorevich Arnold with admiration

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 258, pp. 58–69.

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Gusein-Zade, S.M., Luengo, I. & Melle-Hernández, A. On the power structure over the Grothendieck ring of varieties and its applications. Proc. Steklov Inst. Math. 258, 53 (2007). https://doi.org/10.1134/S0081543807030066

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  • DOI: https://doi.org/10.1134/S0081543807030066

Keywords

  • Modulus Space
  • STEKLOV Institute
  • Conjugacy Class
  • Power Structure
  • Wreath Product