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The Hirzebruch-Mumford volume for the orthogonal group and applications

Valery Gritsenko·Klaus Hulek·G. K. Sankaran
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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 Γis 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(Γ) 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.

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Valery Gritsenko, Klaus Hulek, G. K. Sankaran. 2006-09-27. The Hirzebruch-Mumford volume for the orthogonal group and applications. https://arxiv.org/abs/math/0512595

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