Unlikely intersections in the Torelli locus and the G-functions method

Consider a smooth irreducible Hodge generic curve \(S\) defined over \(\bar{\Q}\) in the Torelli locus \(T_g\subset \mathcal{A}_g\). We establish Zilber-Pink-type statements for such curves depending on their intersection with the boundary of the Baily-Borel compactification of \(\mathcal{A}_g\). For example, when our curve intersects the \(0\)-dimensional stratum of this boundary and \(g\) is odd, we show that there are only finitely many points in the curve for which the corresponding Jacobian variety is non-simple. These results follow as a special case of height bounds for exceptional points in \(1\)-parameter variations of geometric Hodge structures via André's G-functions method, which we extend here to the setting of such variations of odd weight.