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1: Suppose $A_3 $ is the moduli space of abelian varieties of dimension 3 .Is the union of all one dimension shimura varieties in $A_3 $ connected?

2: Given a Shimura curve (explicit construction), can we decide what kind of CM point can occur in this Shimura curve?

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Could you be more precise about what you mean by a "Shimura curve" inside $\mathcal{A}_g$? E.g., do you just mean a one-dimensional Shimura subvariety, or do you possibly really want $g = 2$ and are just talking about Shimura curves associated to quaternion algebras over $\mathbb{Q}$? –  Pete L. Clark Jul 29 '10 at 14:36
(Assuming you mean the latter, I can answer this question, but I probably won't get to it for a little while because I have a three hour lecture to give in less than three hours. There are other regulars here who know the answer; if not, I'll come back later today...) –  Pete L. Clark Jul 29 '10 at 14:38
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