Mathematics – Algebraic Geometry
Scientific paper
2005-07-14
Mathematics
Algebraic Geometry
Some result is improved and some proof simplified. Latex, 23 pages
Scientific paper
To every morphism $\chi\colon L\to M$ of differential graded Lie algebras we associate a functors of artin rings $\Def_\chi$ whose tangent and obstruction spaces are respectively the first and second cohomology group of the cylinder 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 Kaehler manifold is annihilated by the semiregularity map.
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