Calabi-Yau manifolds and generic Hodge groups

TL;DR

This paper investigates the possible generic Hodge groups of Calabi-Yau 3-manifolds with one-dimensional moduli, classifies all potential real forms, and analyzes known examples to understand their Hodge structures.

Contribution

It provides a complete classification of the generic Hodge groups for these Calabi-Yau manifolds and determines their real forms in known cases.

Findings

Complete list of possible generic Hodge groups for the manifolds.

Determination of the real forms of these groups in known examples.

Insight into the structure of Hodge groups in Calabi-Yau 3-manifolds.

Abstract

We study the generic Hodge groups $\Hg(\sX)$ of local universal deformations $\sX$ of Calabi-Yau 3-manifolds with onedimensional complex moduli, give a complete list of all possible choices for $\Hg(\sX)_{\R}$ and determine the latter real groups for known examples.