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

31 pages

References in corpus (1)

• Disproof of modularity of moduli space of CY 3-folds of double covers of P3 ramified along eight planes in general positions

Cited by in corpus (8)

• A strong hyperbolicity property of locally symmetric varieties
• Semi-algebraic horizontal subvarieties of Calabi-Yau type
• Arakelov-Nevanlinna inequalities for variations of Hodge structures and applications
• On the monodromy of the moduli space of Calabi-Yau threefolds coming from eight planes in ${\mathbb{P}}^3$
• Hodge Representations
• Normal Functions over Locally Symmetric Varieties
• The Attractor Conjecture for Calabi-Yau variations of Hodge structures
• The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense