Geodesic
The Kodaira dimension of Siegel modular varieties of genus 3 or higher
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 749-776

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Zbl MR
We consider the moduli space $A_{\text{pol}}(n)$ of (non-principally) polarised abelian varieties of genus $g \geq 3$ with coprime polarisation and full level-n structure. Based upon the analysis of the Tits building in [S], 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. 
Schellhammer, Eric. The Kodaira dimension of Siegel modular varieties of genus 3 or higher. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 749-776. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a15/
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     title = {The {Kodaira} dimension of {Siegel} modular varieties of genus 3 or higher},
     journal = {Bollettino della Unione matematica italiana},
     pages = {749--776},
     year = {2006},
     volume = {Ser. 8, 9B},
     number = {3},
     zbl = {1182.14017},
     mrnumber = {2274125},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a15/}
}
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