Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition

Daniel Huybrechts

arxiv: math/0102116 · v2 · submitted 2001-02-15 · 🧮 math.AG

Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition

Daniel Huybrechts This is my paper

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keywords kaehleralgebradecompositionformsharmonicinfinitesimalinfinitesimallylefschetz

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This paper studies the infinitesimal variation of the Lefschetz decomposition associated with a compatible sl_2-representation on a graded algebra. This allows to prove that the Jordan-Lefschetz property holds infinitesimally for the Kaehler Lie algebra (introduced by Looijenga and Lunts) of any compact Kaehler manifold. As a second application we describe how the space of harmonic forms changes when a Ricci-flat Kaehler form is deformed infinitesimally.

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