On the L-infinity description of the Hitchin Map

Abstract

Recently, E.Martinengo obtained results on obstructions to deformations of Higgs pairs by describing an L-infinity morphism inducing the Hitchin map. In this note we show that analogous results hold for principal G-Higgs bundles, where G is a complex reductive group. We show that the L-infinity morphism has a Lie-algebraic analogue inducing the adjoint quotient morphism.

12 pages. Comments welcome! Exposition improved. References added. Section 3 expanded and corrected. Typos fixed and some conventions adjusted

References in corpus (4)

• Deformation quantization of Poisson manifolds, I
• Deformation theory via differential graded Lie algebras
• Lectures on deformations of complex manifolds
• L-infinity structures on mapping cones