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, p. 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
@article{ASNSP_2007_5_6_4_631_0,
     author = {Manetti, Marco},
     title = {Lie description of higher obstructions to deforming submanifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {4},
     year = {2007},
     pages = {631-659},
     zbl = {1174.13021},
     mrnumber = {2394413},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2007_5_6_4_631_0}
}
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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