Limit mixed Hodge structures of hyperkähler manifolds

Abstract

This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. 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.

arXiv comment12 pages; improved the exposition in sections 3.1 - 3.3; to appear in Mosc. Math. J