  We compute the microscopic entropy of certain 4 and 5 dimensional extermal
black holes which arise for compactification of M-theory and type IIA on
Calabi-Yau 3-folds. The results agree with macroscopic predictions, including
some subleading terms. The macroscopic entropy in the 5 dimensional case
predicts a surprising growth in the cohomology of moduli space of holomorphic
curves in Calabi-Yau threefolds which we verify in the case of elliptic
threefolds.
