The Analogue of Dedekind Eta Functions for Calabi-Yau Manifilolds II.   (Algebraic, Analytic Discriminants and the Analogue of Baily-Borel   Compactification of the Moduli Space of CY Manifolds.)
  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. 
Andrey Todorov