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

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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Correspondence to S. M. Gusein-Zade.

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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