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

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To every morphism χ:L→M 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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     author = {Manetti, Marco},
     title = {Lie description of higher obstructions to deforming submanifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {631--659},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {4},
     year = {2007},
     mrnumber = {2394413},
     zbl = {1174.13021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_4_631_0/}
}
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Manetti, Marco. Lie description of higher obstructions to deforming submanifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 4, pp. 631-659. http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_4_631_0/