On generating series of classes of equivariant Hilbert schemes of fat points

2009/05/12 by S. M. Gusein‐Zade, S. M. Gusein-Zade, I. Luengo +5
Mathematics · #14C05 #14G10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14C05 #msc:14G10

paper · pdf · doi:10.48550/arxiv.0905.1779

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

Abstract

In previous papers the authors gave formulae for generating series of classes (in the Grothendieck ring of complex quasi-projective varieties) of Hilbert schemes of zero-dimensional subschemes on smooth varieties and on orbifolds in terms of certain local data and the, so called, power structure over the corresponding ring. Here we give an analogue of these formulae for equivariant (with respect to an action of a finite group on a smooth variety) Hilbert schemes of zero-dimensional subschemes and compute some local generating series for an action of the cyclic group on a smooth surface.

Citations

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

Related

• Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points
• Generating series of classes of Hilbert schemes of points on orbifolds
• Generating series in the cohomology of Hilbert schemes of points on surfaces
• On the power structure over the Grothendieck ring of varieties and its applications
• On the motive of the Hilbert scheme of points on a surface