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This article is cited in 1 scientific paper (total in 1 paper)
Hodge numbers of generalized Kummer schemes via relative power structures
Andrew Morrisona, Junliang Shenb a Departement Mathematik, ETH Zürich
b Department of Mathematics, Yale University
Abstract:
We develop a power structure over the Grothendieck ring of varieties relative to an abelian monoid, which provides a systematic method to compute the class of the generalized Kummer scheme in the Grothendieck ring of Hodge structures. 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.
Key words and phrases:
power structure, Hodge polynomial, Donaldson–Thomas invariant, generalized Kummer scheme.
Citation:
Andrew Morrison, Junliang Shen, “Hodge numbers of generalized Kummer schemes via relative power structures”, Mosc. Math. J., 21:4 (2021), 807–830
Linking options:
https://www.mathnet.ru/eng/mmj814 https://www.mathnet.ru/eng/mmj/v21/i4/p807
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Abstract page: | 51 | References: | 16 |
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