Calabi-Yau manifolds of some special forms

Let M=M₁×...×M_m be a product of Kähler C-spaces with second Betti numbers b₂(M_i)=1 (1im). The work establishes that the complete intersections X of M produce a finite number of N-dimensional Calabi-Yau manifolds. Moreover, if b₄(M_i)=1, then the complete intersections with vanishing first Pontrjagin classes are finitely many, as well.On the other hand, we consider hypersurfaces of weighted projective spaces and give an explicit formula for their Euler characteristics. As in the previous case, it turns out that only a finite number of these are Calabi-Yau manifolds.