Limit mixed Hodge structures of hyperkähler manifolds

This note is inspired by the work of Deligne. We study limit mixed Hodge structures of degenerating families of compact hyperkähler manifolds. We show that when the monodromy action on $H^2$ has maximal index of unipotency, the limit mixed Hodge structures on all cohomology groups are of Hodge–Tate type.