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∞-morphism and, by standard facts about L∞-algebras, we obtain new conditions on obstructions to deform Hitchin pairs.
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