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arXiv · 1505.02989

Motivic classes of generalized Kummer schemes via relative power structures

Andrew Morrison·Junliang Shen
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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.

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Andrew Morrison, Junliang Shen. 2015-05-12. Motivic classes of generalized Kummer schemes via relative power structures. https://arxiv.org/abs/1505.02989

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