Mathematical Research Letters

Volume 28 (2021)

Number 2

On the Hodge structures of compact hyperkähler manifolds

Pages: 623 – 635



Andrey Soldatenkov (Institut für Mathematik, Humboldt-Universität zu Berlin, Germany)


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 hyperkähler 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.

Received 24 June 2019

Accepted 12 November 2019

Published 13 May 2021