A realization for a $\mathbb{Q}$-Hermitian variation of Hodge structure of Calabi-Yau type with real multiplication

TL;DR

This paper demonstrates how certain rational variations of Hodge structure of Calabi-Yau type can be realized as sub-variations within structures associated to abelian varieties of Weil type, linking complex geometry and algebraic structures.

Contribution

It provides a new realization of rational Hodge structures of Calabi-Yau type via sub-variations connected to abelian varieties of Weil type.

Findings

Rational descents of Calabi-Yau type variations are realizable as sub-variations.

Connections established between Hodge structures and abelian varieties of Weil type.

Enhances understanding of the structure of Calabi-Yau variations over tube domains.

Abstract

We show that the $\mathbb{Q}$-descents of the canonical $\mathbb{R}$-variation of Hodge structure of Calabi-Yau type over a tube domain of type $A$ can be realized as sub-variations of Hodge structure of certain $\mathbb{Q}$-variations of Hodge structure which are naturally associated to abelian varieties of (generalized) Weil type.