Description
In this talk, I would like to discuss the joint deformation problem of a Kahler manifold and a Higgs bundle.
I will introduce the DGLA which governs this deformation problem.
Moreover, I will show that if the Higgs bundle is polystable with zero Chern classes, the Kuraishi space of pair (Higgs bundle, Kahler manifold) is isomorphic to the Kuranishi space of (Higgs bundle) x the Kuranishi space of (Higgs bundle) using the property of the DGLA.