  In this paper we construct the analogue of Dedekind eta-function on the
moduli space of polarized CY manifolds. We prove that the L-two norm of eta is
the regularized determinants of the Laplacians of the CY metric on (0,1) forms.
We construct the analogue of the Baily-Borel Compactification of the moduli
space of polarized CY and prove that it has the same properties as the
Baily-Borel compactification of the locally symmetric Hermitian spaces. We
proved that the compactification constructed in the paper is the minimal.
