Finiteness of stable orthogonal modular varieties of non-general type

Abstract

We prove that there are only finitely many even lattices L of signature (2,n) with n>14 such that the modular variety defined by the stable orthogonal group of L is not of general type.

arXiv commentThe previous version contained a serious error in the final paragraph of Section 3, which is bypassed in the current version

References in corpus (3)

• Reflective modular forms in algebraic geometry
• Uniruledness of orthogonal modular varieties
• E8 lattice and the Kodaira dimension of orthogonal modular varieties

Cited by in corpus (2)

• On the Kodaira dimension of orthogonal modular varieties
• Finiteness of 2-reflective lattices of signature (2,n)