On the Hodge structures of compact hyperkähler manifolds

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 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.

arXiv comment8 pages. Includes a more precise version of Theorem 3.6 and other minor corrections. To appear in Math. Res. Lett

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