Lie cylinders and higher obstructions to deforming submanifolds
-- Marco Manetti

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To every morphism chi: L --> M of differential graded
Lie algebras we associate a functor of artin rings Def_chi
whose tangent and obstruction spaces are respectively the first
and second cohomology group of the cylinder of chi.  Such a
construction applies to Hilbert and Brill-Noether functors and
allows us to prove with ease that every higher obstruction to
deforming a smooth submanifold of a K&auml;hler manifold is
annihilated by the semiregularity map.