Decomposition of Jacobians and Shimura subvarieties of $$A_g$$

Abstract Using the decomposition of Jacobians with group action, we prove the non-existence of some Shimura subvarieties in the moduli space of ppav $$A_{g}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> arising from families of dihedral and quaternionic covers of the complex projective line $${{\mathbb {P}}}^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> </mml:math> .