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THE KUGA–SATAKE CONSTRUCTION UNDER DEGENERATION

Part of: Families, fibrations

Published online by Cambridge University Press:  17 May 2019

Stefan Schreieder  and
Andrey Soldatenkov
Stefan Schreieder
Affiliation:
Mathematisches Institut, LMU München, Theresienstr. 39, 80333München, Germany (schreieder@math.lmu.de)
Andrey Soldatenkov
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099Berlin, Germany (soldatea@hu-berlin.de)
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Abstract

We extend the Kuga–Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga–Satake abelian varieties associated with polarized variations of K3 type Hodge structures over the punctured disc.

Keywords

Hodge structureK3 surfaceabelian varietylimit mixed Hodge structure

MSC classification

Primary: 14D06: Fibrations, degenerations 14D07: Variation of Hodge structures
Secondary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 6 , November 2020 , pp. 2165 - 2182
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Copyright
© Cambridge University Press 2019

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Footnotes

The authors are supported by the SFB/TR 45 ‘Periods, Moduli Spaces and Arithmetic of Algebraic Varieties’ of the DFG (German Research Foundation).

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