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arXiv · 1701.03225

On the Kodaira dimension of orthogonal modular varieties

Shouhei Ma
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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.

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Shouhei Ma. 2017-01-12. On the Kodaira dimension of orthogonal modular varieties. https://doi.org/10.1007/s00222-017-0781-x

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