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Lie description of higher obstructions to deforming submanifolds

Marco Manetti
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Abstract

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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Marco Manetti. 2005-07-14. Lie description of higher obstructions to deforming submanifolds. https://doi.org/10.2422/2036-2145.2007.4.06

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