Polarized Variation of Hodge Structures of Calabi-Yau Type and Characteristic Subvarieties Over Bounded Symmetric Domains

In this paper we extend the construction of the canonical polarized variation of Hodge structures over tube domain considered by B. Gross in \cite{G} to bounded symmetric domain and introduce a series of invariants of infinitesimal variation of Hodge structures, which we call characteristic subvarieties. We prove that the characteristic subvariety of the canonical polarized variations of Hodge structures over irreducible bounded symmetric domains are identified with the characteristic bundles defined by N. Mok in \cite{M}. We verified the generating property of B. Gross for all irreducible bounded symmetric domains, which was predicted in \cite{G}.