The Kodaira dimension of Siegel modular varieties of genus 3 or higher
Abstract
We consider the moduli space Apol(n) of (non-principally) polarised abelian varieties of genus g≥3 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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