On the Weil-Petersson volume and the first Chern Class of the moduli   space of Calabi-Yau manifolds
  In this paper, we proved that the Weil-Petersson volume of Calabi-Yau moduli is a rational number. We also proved that the integrations of the invariants of the Ricci curvature of the Weil-Petersson metric with respect to the Weil-Petersson volume form are all rational numbers. 
Zhiqin Lu and Xiaofeng Sun