On the Hodge structures of compact hyperkähler manifolds

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.

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Received 24 June 2019

Accepted 12 November 2019

Published 13 May 2021