Universal variations of Hodge structure and Calabi-Yau Schottky relations

Abstract

This paper is a sequel to math.AG/9810041 (whose abstract should have mentioned the fact that a version of the jacobi complex and higher-order Kodaira-Spencer maps were also discovered independently by Esnault and Viehweg). We give a canonical algebraic construction for the variation of Hodge structure associated to the universal m-th order deformation of a compact Kahler manifold without vector fields. Specializing to the case of a Calabi-Yau manifold, we give a formula for the mth derivative of its period map and deduce formal defining equations for the image (Schottky relations).