Seiberg-Witten differentials on the Hitchin base

TL;DR

This paper explicitly describes the covariant derivative of the Seiberg-Witten differential on the Hitchin base using Lie theory and cameral data, enhancing understanding of the geometric structures involved.

Contribution

It provides a detailed Lie-theoretic and cameral data description of the covariant derivative of the Seiberg-Witten differential on the Hitchin base.

Findings

Explicit formula for the covariant derivative in terms of Lie theory.

Connection between Seiberg-Witten differentials and Hitchin fibration.

Enhanced geometric understanding of the Hitchin base structures.

Abstract

In this note we describe explicitly, in terms of Lie theory and cameral data, the covariant (Gauss--Manin) derivative of the Seiberg--Witten differential defined on the weight-one variation of Hodge structures that exists on a Zariski open subset of the base of the Hitchin fibration. Dedicated to Tony Pantev on the occasion of his 60th birthday.