A famous conjecture from Coleman and Oort says that for genus g greater than 0 there do not exist positive dimensional special subvarieties of A_g generically contained in the Torelli locus. Firstly we will give a brief introduction to the characters of this conjecture. Then we will describe how the examples of totally geodesic subvarieties of A_g known so far are obtained as families of Jacobians of Galois coverings f: C to C’, where the genus of C’ is g’=0,1. We will show that all these examples satisfy a sufficient condition that we will explain. Finally, we will see that this condition gives us a bound on g’.
