The locus of real multiplication and the Schottky locus
  We prove that the generic point of a Hilbert modular four-fold is not a Jacobian. The proof uses degeneration techniques and is independent of properties of the mapping class group used in preceding papers on locally symmetric subvarieties of the moduli space of abelian varieties contained in the Schottky locus. 
Matt Bainbridge and Martin M\"oller
math.AG