On holomorphic sections of Veech holomorphic families of Riemann   surfaces
  We give upper bounds of the numbers of holomorphic sections of Veech holomorphic families of Riemann surfaces. The numbers depend only on the topological types of base Riemann surfaces and fibers. We also show a relation between types of Veech groups and moduli of cylinder decompositions of flat surfaces. 
Yoshihiko Shinomiya
math.CV