论文标题
Torelli基因座和G功能方法中不太可能
Unlikely intersections in the Torelli locus and the G-functions method
论文作者
论文摘要
考虑在torelli locus $ \ bar {\ q} $上定义的平滑不可约的hodge通用曲线$ s $ s $，我们根据$ \ Mathcal {a} _g $的Baily-borel cartactification的边界建立了此类曲线的Zilber-Pink-type语句。例如，当我们的曲线与该边界的$ 0 $维层和$ g $相交时，我们表明曲线中只有许多点有限的点，相应的Jacobian品种是非简单的。 这些结果是通过安德烈（André）的G-功能方法在几何杂货结构的$ 1 $参数变化中的特殊情况的特殊情况，我们将其扩展到此处，以设置这种奇数变化的设置。
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.
