On the Kodaira dimension of orthogonal modular varieties
Algebraic Geometry
2018-07-04 v1 Number Theory
Representation Theory
Abstract
We prove that up to scaling there are only finitely many integral lattices L of signature (2,n) with n>20 or n=17 such that the modular variety defined by the orthogonal group of L is not of general type. In particular, when n>107, every modular variety defined by an arithmetic group for a rational quadratic form of signature (2,n) is of general type. We also obtain similar finiteness in n>8 for the stable orthogonal groups. As a byproduct we derive finiteness of lattices admitting reflective modular form of bounded vanishing order, which proves a conjecture of Gritsenko and Nikulin.
Keywords
Cite
@article{arxiv.1701.03225,
title = {On the Kodaira dimension of orthogonal modular varieties},
author = {Shouhei Ma},
journal= {arXiv preprint arXiv:1701.03225},
year = {2018}
}
Comments
essentially superseding 1309.7121