Infinitesimal deformations of Hitchin pairs and Hitchin map

TL;DR

This paper studies the infinitesimal deformation theory of Hitchin pairs and the Hitchin map, using differential graded Lie algebras and L-infinity morphisms to refine understanding of deformations and obstructions.

Contribution

It identifies controlling dglas for deformations of Hitchin pairs and shows the Hitchin map arises from an L-infinity morphism, providing new insights into obstructions.

Findings

Controlled deformations via specific dglas.

Hitchin map induced by a natural L-infinity morphism.

New conditions on obstructions to deform Hitchin pairs.

Abstract

We identify dglas that control infinitesimal deformations of the pairs (manifold, Higgs bundle) and of Hitchin pairs. As a consequence, we recover known descriptions of first order deformations and we refine known results on obstructions. Secondly we prove that the Hitchin map is induced by a natural L-infinity morphism and, by standard facts about L-infinity algebras, we obtain new conditions on obstructions to deform Hitchin pairs.