Bounding integral points on the Siegel modular variety A_2(2).

We determine two explicit upper bounds for the stable Faltings height of principally polarised abelian surfaces over number fields corresponding to S-integral points on the Siegel modular variety A_2(2). One upper bound, using Runge's method, is uniform in S as long as |S|<3; the other, using Baker's method, is not uniform but allows |S|<10. Our application of a higher-dimensional Baker's method is completely explicit and improves upon the general case due to Levin.