Some remarks on special K\"ahler geometry

TL;DR

This paper provides a new, direct proof of the relationship between quaternionic structures on cotangent bundles of special Kähler manifolds and variations of Hodge structures on their complexified tangent bundles.

Contribution

It introduces a novel, direct proof connecting quaternionic geometry and Hodge theory in the context of special Kähler manifolds.

Findings

Established a direct proof of the relationship between quaternionic structures and Hodge variations.

Clarified the geometric interplay in special Kähler geometry.

Enhanced understanding of the structure of cotangent bundles in this setting.

Abstract

Given a special Kahler manifold M, we give a new, direct proof of the relationship between the quaternionic structure on its cotangent bundle and the variation of Hodge structures on the complexification of TM.