On the Kodaira Dimension of the Moduli of Deformation Generalised Kummer Varieties

Abstract

We prove general type results for orthogonal modular varieties associated with the moduli of compact hyperkähler manifolds of deformation generalised Kummer type ('deformation generalised Kummer varieties'). In particular, we consider moduli spaces of deformation generalised Kummer fourfolds with split-polarisation of degree $2d$. Our main result is that when $d$ is prime or $2d$ is square-free then the associated modular varieties are of general type when $d$ exceeds bounds we determine, subject to the existence of certain low-weight cusp forms for $O(2,n)$. As a corollary, we conclude that the corresponding moduli spaces are also of general type.

The Jacobi form constructions for low-weight cusp forms in v3 have been replaced with an argument based on studying vector-valued modular forms using Skoruppa's dimension formula. To appear in 'Algebraic Geometry'. 62 pages

References in corpus (3)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• On the Kodaira dimension of orthogonal modular varieties
• On the monodromy of moduli spaces of sheaves on K3 surfaces II

Cited by in corpus (1)

• General type results for moduli of deformation generalised Kummer varieties