The Hirzebruch-Mumford volume for the orthogonal group and applications
Number Theory
2007-05-23 v3 Algebraic Geometry
Abstract
In this paper we derive an explicit formula for the Hirzebruch-Mumford volume of an indefinite lattice L of rank at least 3. If \Gamma is an arithmetic subgroup of the group O(L) of isometries of L and L has signature (2,n), then an application of Hirzebruch-Mumford proportionality allows us to determine the leading term of the growth of the dimension of the spaces S_k(\Gamma) of cusp forms of weight k, as k goes to infinity. We compute this in a number of examples, which are important for geometric applications.
Keywords
Cite
@article{arxiv.math/0512595,
title = {The Hirzebruch-Mumford volume for the orthogonal group and applications},
author = {Valery Gritsenko and Klaus Hulek and G. K. Sankaran},
journal= {arXiv preprint arXiv:math/0512595},
year = {2007}
}
Comments
Minor corrections, bibliography updated