The Torelli locus and special subvarieties

Abstract

We study the Torelli locus T_g in the moduli space A_g of abelian varieties. We consider special subvarieties (Shimura subvarieties) contained in the Torelli locus. We review the construction of some non-trivial examples, and we discuss some conjectures, techniques and recent progress.

To appear in the Handbook of Moduli (G. Farkas, I. Morrison, eds.)

References in corpus (1)

• On Hrushovski's proof of the Manin-Mumford conjecture

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• The fibers of the ramified Prym map
• The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds
• Normal Functions over Locally Symmetric Varieties
• A note on Shimura subvarieties in the hyperelliptic Torelli locus
• Some evidence for the Coleman-Oort conjecture
• Endomorphism algebras of factors of certain hypergeometric Jacobians
• On Higgs bundles over Shimura varieties of ball quotient type
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• Moduli spaces and algebraic cycles in real algebraic geometry
• Abelian covers and second fundamental form
• On large prime actions on Riemann surfaces
• On the height of Gross-Schoen cycles in genus three
• Spanning the isogeny class of a power of an ordinary elliptic curve over a finite field. Application to the number of rational points of curves of genus $\le 4$
• Ekedahl-Oort strata of curves of genus four in characteristic three