General type results for moduli of deformation generalised Kummer varieties

Matthew Dawes

Mathematische Nachrichten, 2025, vol. 298, issue 10, 3376-3393

Abstract: In Dawes [Algebr. Geom. 12(2025), no. 3, 601–660], families of orthogonal modular varieties F(Γ)$\mathcal {F}(\Gamma)$ associated with moduli spaces of compact hyperkähler manifolds of deformation generalized Kummer type (also known as “deformation generalized Kummer varieties”) were studied. The orthogonal modular varieties were defined for an even integer 2d$2d$, corresponding to the degree of polarization of the associated hyperkähler manifolds. It was shown in Dawes [Algebr. Geom. 12(2025), no. 3, 601–660] that the modular varieties are of general type when 2d$2d$ is square‐free and sufficiently large. The purpose of this paper is to show that the square‐free condition can be removed.

Date: 2025
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