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

TL;DR

This paper extends the construction of polarized variations of Hodge structures to bounded symmetric domains, introduces characteristic subvarieties as invariants, and confirms their properties aligning with prior predictions.

Contribution

It generalizes Gross's construction to all irreducible bounded symmetric domains and identifies characteristic subvarieties with Mok's characteristic bundles.

Findings

Characteristic subvarieties coincide with Mok's characteristic bundles.

Confirmed Gross's generating property for all irreducible bounded symmetric domains.

Extended Hodge structure constructions to a broader class of domains.

Abstract

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}.