Abstract

To every morphism $\chi \colon L\rightarrow M$ of differential graded Lie algebras we associate a functors of artin rings $\operatorname{Def}_\chi $ whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of $\chi $. Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kähler manifold is annihilated by the semiregularity map