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Moscow Mathematical Journal, 2020, Volume 20, Number 2, Pages 423–436
DOI: https://doi.org/10.17323/1609-4514-2020-20-2-423-436 (Mi mmj771) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Limit mixed Hodge structures of hyperkähler manifolds

Andrey Soldatenkov

Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin
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DOI: https://doi.org/10.17323/1609-4514-2020-20-2-423-436
Abstract: 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.
Key words and phrases: hodge structure, limit mixed Hodge structure, hyperkähler manifold.
Funding agency Grant number
Deutsche Forschungsgemeinschaft SFB/TR 45
The author was supported by the SFB/TR 45 `Periods, Moduli Spaces and Arithmetic of Algebraic Varieties' of the DFG (German Research Foundation).
Bibliographic databases:
Document Type: Article
MSC: Primary 14D06, 14D07; Secondary 14D05
Language: English
Citation: Andrey Soldatenkov, “Limit mixed Hodge structures of hyperkähler manifolds”, Mosc. Math. J., 20:2 (2020), 423–436
Citation in format AMSBIB
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\paper Limit mixed Hodge structures of hyperk\"ahler manifolds
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