On deformations of pairs (manifold, coherent sheaf)
We analyse infinitesimal deformations of pairs $(X,sF)$ with $sF$ a coherent sheaf on a smooth projective variety $X$ over an algebraically closed field of characteristic $0$. We describe a differential graded Lie algebra controlling the deformation problem, and we prove an analog of a Mukai-Artamkin Theorem about the trace map.