On the Cartwright-Steger surface
  In this article, we study various concrete algebraic and differential geometric properties of the Cartwright-Steger surface. In particular, we determine the genus of a generic fiber of the Albanese fibration, and deduce that the singular fibers are not totally geodesic, answering an open problem about fibrations of a complex ball quotient over a Riemann surface. 
Donald I. Cartwright, Vincent Koziarz and Sai-Kee Yeung
math.AG math.CV