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Cohomological constraint on deformations of compact Kaehler manifolds
No full textWe prove that for every compact K\"ahler manifold the cup product can be lifted to an L_{\oo}-morphism from the Kodaira-Spencer differential graded Lie algebra to the suspension of the space of linear endomorphisms of the singular cohomology of . As a consequence we get an algebraic proof of the principle ``obstructions to deformations of compact K\"{a}hler manifolds annihilate ambient cohomology''
Lie description of higher obstructions to deforming submanifolds
Full text linkTo every morphism chi : L -> M of differential graded Lie algebras we associate a functors of artin rings Def chi whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of chi. 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 Kahler manifold is annihilated by the semiregularity map
Corso introduttivo alla geometria algebrica
No full textAppunti dei corsi tenuti dai docenti della Scuola Normale Superiore di Pis
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