To every morphism of differential graded Lie algebras we associate a functors of artin rings whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of . 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.
@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}, 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://www.numdam.org/item/ASNSP_2007_5_6_4_631_0/} }
TY - JOUR AU - Manetti, Marco TI - Lie description of higher obstructions to deforming submanifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 631 EP - 659 VL - 6 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2007_5_6_4_631_0/ LA - en ID - ASNSP_2007_5_6_4_631_0 ER -
%0 Journal Article %A Manetti, Marco %T Lie description of higher obstructions to deforming submanifolds %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 631-659 %V 6 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2007_5_6_4_631_0/ %G en %F 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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