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Extended period domains, algebraic groups, and higher Albanese manifolds

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arxiv 1611.03179 v2 pith:7H7Q3ETK submitted 2016-11-10 math.AG

Kazuya Kato , Chikara Nakayama , Sampei Usui This is my paper · ORCID
classification math.AG
keywords domainsperiodalbanesealgebraiccompactificationsextendedhighermanifolds
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For a linear algebraic group G over the field of rational numbers, we consider the period domains D classifying G-mixed Hodge structures, and construct the extended period domains as toroidal partial compactifications. We give an interpretation of higher Albanese manifolds by Hain and Zucker by using the above D for some G, and extend them via the toroidal partial compactifications.

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  1. O-minimal geometry of higher Albanese manifolds

    math.AG 2025-05 conditional novelty 8.0 of 10

    Higher Albanese manifolds and maps are definable in o-minimal structures, and if a higher Albanese manifold of level at least three is algebraic, the tower stabilises at step two, making the pro-unipotent fundamental ...

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