Locally symmetric families of curves and jacobians

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This paper addresses the following question of Oort: "Are there any postive dimensional locally symmetric subvarieties of the moduli space of abelian varieties that are contained in the jacobian locus and contain the jacobian of at least one smooth curve? Some partial results are given.
15 pages, AMS-LaTeX. This has appeared in the book Moduli of Curves and Abelian Varieties, edited by Carel Faber and Eduard Looijenga, Aspects of Mathematics, Vieweg, Wiesbaden 1999, 91--108. This is the published version. Some proofs have been lengthened and typos corrected

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