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The Euler characteristics of generalized Kummer schemes

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Abstract

We compute the Euler characteristics of the generalized Kummer schemes associated to \(A\times Y\), where A is an abelian variety and Y is a smooth quasi-projective variety. When Y is a point, our results prove a formula conjectured by Gulbrandsen.

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Notes

  1. Since we mainly concern Euler characteristics, we can always work with the reduced scheme structure in this paper.

  2. After my talk on the results of this paper at the workshop “Motivic invariants related to K3 and abelian geometries” in Berlin, I was informed by Andrea Ricolfi that he obtained the formula when Y is a point and A is an abelian threefold independently.

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Acknowledgments

I would like to thank my advisor Rahul Pandharipande for his support, encouragement and helpful conversations. Thanks also to Andrew Morrison, Georg Oberdieck, and Qizheng Yin for related discussions, to Jim Bryan for an inspiring talk in the moduli seminar at ETH Zürich, and to the referee for comments and suggestions. This work was carried out in the group of Pandharipande at ETH Zürich, supported by grant ERC-2012-AdG-320368-MCSK.

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  1. Departement Mathematik, ETH Zürich, Zurich, Switzerland

    Junliang Shen

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  1. Junliang Shen
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Correspondence to Junliang Shen.

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Shen, J. The Euler characteristics of generalized Kummer schemes. Math. Z. 281, 1183–1189 (2015). https://doi.org/10.1007/s00209-015-1526-4

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