Mathematics – Algebraic Geometry
Scientific paper
2001-05-22
Adv. Math. 186 (2004) 125-142.
Mathematics
Algebraic Geometry
Latex-10 pages
Scientific paper
We prove that for every compact K\"ahler manifold $X$ there exists an $L$-infinity morphism, lifting the usual cup product in cohomology, from the Kodaira-Spencer differential graded Lie algebra to the suspension of the space of linear endomorphisms of the singular cohomology of $X$. As a consequence we get an algebraic proof of the principle ``obstructions to deformations of compact Kaehler manifolds annihilate ambient cohomology''.
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