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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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, 53–64 (2007). https://doi.org/10.1134/S0081543807030066
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DOI: https://doi.org/10.1134/S0081543807030066