English

Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition

Algebraic Geometry 2007-05-23 v2

Abstract

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.

Keywords

Cite

@article{arxiv.math/0102116,
  title  = {Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition},
  author = {Daniel Huybrechts},
  journal= {arXiv preprint arXiv:math/0102116},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T16:37:20.572Z