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.

中文翻译：

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关于紧凑型超khähler流形的霍奇结构

本说明的目的是说明一个著名的民俗结果：紧致超kähler流形第二同调上的Hodge结构唯一地确定了所有更高同调组上的Hodge结构。在文献中很难找到。