Abstract
Let X be an Abelian threefold. We prove a formula, conjectured by the first author, expressing the Euler characteristic of the generalized Kummer schemes \(K^nX\) of X in terms of the number of plane partitions. This computes the Donaldson–Thomas invariant of the moduli stack \([K^nX/X_n]\).
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References
Andrews, G.E.: The Theory of Partitions. Cambridge University Press, Cambridge (1998)
Cheah, J.: On the cohomology of Hilbert schemes of points. J. Algebraic Geom. 5(3), 479–511 (1996)
Debarre, O.: On the Euler characteristic of generalized Kummer varieties. Am J Math 121(3), 577–586 (1999)
Ellingsrud, G., Strømme, S.A.: On the homology of the Hilbert scheme of points in the plane. Invent. Math. 87, 343–352 (1987)
Gusein-Zade, S.M., Luengo, I., Melle-Hernández, A.: Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points. Mich. Math. J. 54(2), 353–359 (2006)
Gulbrandsen, M.G.: Computing the Euler characteristic of generalized Kummer varieties. Ark. Mat. 45(1), 49–60 (2007)
Gulbrandsen, M.G.: Donaldson–Thomas invariants for complexes on abelian threefolds. Math. Z.273(1–2), 219–236 (2013)
Shen, J.: The Euler characteristics of generalized Kummer schemes. arXiv:1502.03973
Stanley, R.P.: Enumerative Combinatorics, vol. 2. Cambridge University Press, Cambridge (1999)
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Gulbrandsen, M.G., Ricolfi, A.T. The Euler charateristic of the generalized Kummer scheme of an Abelian threefold. Geom Dedicata 182, 73–79 (2016). https://doi.org/10.1007/s10711-015-0128-y
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DOI: https://doi.org/10.1007/s10711-015-0128-y