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Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition

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arxiv math/0102116 v2 pith:S6DDU2MR submitted 2001-02-15 math.AG

Daniel Huybrechts This is my paper · ORCID
classification math.AG
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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  1. The LLV Algebra for Primitive Symplectic Varieties with Isolated Singularities

    math.AG 2022-11 unverdicted novelty 6.0 of 10

    Extends the LLV algebra to primitive symplectic varieties with isolated singularities via an isomorphism g ≅ so((IH²(X,Q), Q_X) ⊕ h) and studies the resulting representation theory with applications to the P=W conjecture.

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