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The Kodaira dimension of Siegel modular varieties of genus 3 or higher

Eric Schellhammer
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Abstract

We consider the moduli space $A_{pol}(n)$ of (non-principally) polarised abelian varieties of genus $g\geq3$ with coprime polarisation and full level-$n$ structure. Based upon the analysis of the Tits building in math/0405321, we give an explicit lower bound on $n$ that is sufficient for the compactified moduli space to be of general type if one further explicit condition is satisfied.

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Eric Schellhammer. 2004-05-18. The Kodaira dimension of Siegel modular varieties of genus 3 or higher. https://arxiv.org/abs/math/0405349

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