Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition

Details Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition

2001-02-15

arxiv.org/abs/math/0102116v2

Mathematics

Algebraic Geometry

Revised version: Lemma in Sect. 3 corrected, typos corrected, Corollary in Sect. 4 added

Scientific paper

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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