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Abstract A Kodaira fibration is a non‐isotrivial fibration from a smooth algebraic surfaceSto a smooth algebraic curveBsuch that all fibers are smooth algebraic curves of genusg. Such fibrations arise as complete curves inside the moduli space of genusgalgebraic curves. We investigate here the possible connected monodromy groups of a Kodaira fibration in the case and classify which such groups can arise from a Kodaira fibration obtained as a general complete intersection curve inside a subvariety of parametrizing curves whose Jacobians have extra endomorphisms.more » « less
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