TITLE: Connected cycles of Shimura curves in $A_{g}$ not contained in larger Shimura subvarieties
QUESTION [5 upvotes]: Is there always a finite family of Shimura curves $(C_{i})$ in $A_{g}$ the moduli space of principally polarized abelian varieties of dimension $g(\geq 2)$, such that the union $\cup C_{i}$ is connected and such that $\cup C_{i}$ is not strictly contained in larger Shimura subvarieties (special subvarieties) except $A_{g}$ itself? i.e. there does not exist Shimura subvarieties $Z$ in $A_{g}$ with $\cup C_{i}\subsetneq Z$ and $Z\neq A_{g}$? I will appreciate any suggestion of results related to this problem and/or suggestions how one can possibly construct such families.

REPLY [2 votes]: There are countably many special subvarieties because they are defined over $\overline{Q}$
but I do not see how this is relevant to your question?
I understand you want to know whether any Shimura curve is contained in a special subvariety;
I think the answer is yes, it should be contained in an appropriate Hilbert modular variety.