On the Hodge structures of compact hyperk\"ahler manifolds
Algebraic Geometry
2021-05-14 v2
Abstract
The purpose of this note is to give an account of a well-known folklore result: the Hodge structure on the second cohomology of a compact hyperk\"ahler manifold uniquely determines Hodge structures on all higher cohomology groups. We discuss the precise statement and its proof, which are somewhat difficult to locate in the literature.
Cite
@article{arxiv.1905.07793,
title = {On the Hodge structures of compact hyperk\"ahler manifolds},
author = {Andrey Soldatenkov},
journal= {arXiv preprint arXiv:1905.07793},
year = {2021}
}
Comments
8 pages. Includes a more precise version of Theorem 3.6 and other minor corrections. To appear in Math. Res. Lett