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

2006/05/17 by S. M. Gusein‐Zade, S. M. Gusein-Zade, I. Luengo +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #14C05 #14G10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation #math-ph #math.AG #math.MP #msc:14C05 #msc:14G10

paper · pdf · doi:10.48550/arxiv.math/0605467

18 pages

arxiv created 2006/05/17 · openalex publication_date 2006/05/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups

Cited by

• The refined local Donaldson-Thomas theory of curves

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