On the Geometry of Moduli Space of Polarized Calabi-Yau manifolds
  In this paper, we study the Chern classes on the moduli space of polarized Calabi-Yau manifolds. We prove that the integrations of the invariants of the curvature of the Weil-Petersson metric are finite. In some special cases, they are even rational numbers. 
Michael Douglas and Zhiqin Lu