# Characterization of Calabi--Yau variations of Hodge structure over tube domains by characteristic forms

## TL;DR

This paper demonstrates that Sheng and Zuo's characteristic forms uniquely identify Gross's canonical Calabi-Yau type variations of Hodge structure over Hermitian symmetric tube domains, providing a new characterization method.

## Contribution

It establishes that characteristic forms fully characterize Gross's canonical variations of Hodge structure of Calabi-Yau type over tube domains, linking invariants to specific geometric structures.

## Key findings

- Characteristic forms uniquely determine Gross's variations
- Characterization of Calabi-Yau type variations over tube domains
- Link between invariants and geometric structures

## Abstract

Sheng and Zuo's characteristic forms are invariants of a variation of Hodge structure. We show that they characterize Gross's canonical variations of Hodge structure of Calabi-Yau type over (Hermitian symmetric) tube domains.