Infinitesimal deformations of Hitchin pairs and Hitchin map

Details Infinitesimal deformations of Hitchin pairs and Hitchin map Infinitesimal deformations of Hitchin pairs and Hitchin map

2010-03-29

arxiv.org/abs/1003.5531v1

Mathematics

Algebraic Geometry

23 pages, Latex

Scientific paper

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.

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