Lie description of higher obstructions to deforming submanifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 4, pp. 631-659.

To every morphism χ:LM of differential graded Lie algebras we associate a functors of artin rings Def χ whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of χ. 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.

Classification: 13D10, 14D15
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Manetti, Marco. Lie description of higher obstructions to deforming submanifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 4, pp. 631-659. http://www.numdam.org/item/ASNSP_2007_5_6_4_631_0/

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