Moscow Mathematical Journal

Volume 20, Issue 2, April–June 2020  pp. 423–436.

Limit Mixed Hodge Structures of Hyperkähler Manifolds

Authors:  Andrey Soldatenkov (1)
Author institution:(1) Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin

Summary:

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.

2010 Math. Subj. Class. Primary: 14D06, 14D07; Secondary: 14D05.

Keywords: Hodge structure, limit mixed Hodge structure, hyperkähler manifold.