Motivic classes of generalized Kummer schemes via relative power structures

2015/05/12 by Andrew Morrison, Morrison, Andrew, Junliang Shen +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1505.02989

openalex publication_date 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We develop a power structure over the Grothendieck ring of varieties relative to an abelian monoid, which allows us to compute the motivic class of the generalized Kummer scheme. We obtain a generalized version of Cheah's formula for the Hilbert scheme of points, which specializes to Gulbrandsen's conjecture for Euler characteristics. Moreover, in the surface case we prove a conjecture of Göttsche for geometrically ruled surfaces, and we obtain an explicit formula for the virtual motive of the generalized Kummer scheme in dimension three.

Citations

• A geometric invariant of a finite group
• The Grothendieck group of algebraic stacks

Related

• The Euler characteristics of generalized Kummer schemes
• Algebraic cycles on a generalized Kummer variety
• Symmetric powers of null motivic Euler characteristic
• Fundamental Group Schemes of Generalized Kummer Variety
• On the power structure over the Grothendieck ring of varieties and its applications