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.)