Lie description of higher obstructions to deforming submanifolds

Manetti, Marco

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 4, pp. 631-659.

To every morphism $\chi :L\to M$ 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 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.

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