We address the problems of degeneration and curvature. Previously, for moduli of smooth hypersurfaces, a generalized Petersson-Weil metric was introduced, using complete Kaehler-Einstein metrics on the complements. The curvature tensor was computed explicitly, and hyperbolicity followed. For general dimensions, we use a different approach. We compute the asymptotic behavior, show that the Petersson-Weil metric is the curvature of the Quillen metric for certain determinant bundles, and investigate the situation with respect to degenerations. A modification of the Petersson-Weil metric yields a certain hermitian metric on the moduli space, whose curvature is computed.