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 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{BUMI_2006_8_9B_3_a15,
     author = {Schellhammer, Eric},
     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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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/