Cohomological constraint to deformations of compact Kaehler manifolds

Abstract

We prove that for every compact Kähler 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''.

arXiv commentLatex-10 pages

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• Introduction to sh Lie algebras for physicists
• Mirror symmetry and deformation quantization

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• Derived Kodaira Spencer map, Cosection lemma, and semiregularity