On some components of moduli space of surfaces of general type
On smooth curves passing through rational surface singularities.
Normal degenerations of the complex projective plane.
Normal projective surfaces with
Lie description of higher obstructions to deforming submanifolds
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.
On the adjoint map of homotopy abelian DG-Lie algebras
We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.
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