Chern classes and the periods of mirrors
  We show how Chern classes of a Calabi Yau hypersurface in a toric Fano manifold can be expressed in terms of the holomorphic at a maximal degeneracy point period of its mirror. We also consider the relation between Chern classes and the periods of mirrors for complete intersections in Grassmanian Gr(2,5). 
A.Libgober