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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


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, hyperk√§hler manifold.

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