Higher-weight Jacobians
We define and study Jacobians of Hodge structures with weight greater than 1. Jacobians of weight 2 naturally come up in the context of the Brauer group and the Tate conjecture. They were previously studied in a special case by Beauville in his work on surfaces of maximal Picard number, and are rela...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
22.08.2024
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Subjects | |
Online Access | Get full text |
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Summary: | We define and study Jacobians of Hodge structures with weight greater than 1.
Jacobians of weight 2 naturally come up in the context of the Brauer group and
the Tate conjecture. They were previously studied in a special case by
Beauville in his work on surfaces of maximal Picard number, and are related to
the work of Totaro on Hodge structures with no middle pieces. Higher-weight
Jacobians are complex tori, and it is generally quite difficult to tell if they
are algebraic. After discussing some general theory, we compute numerous
examples of Jacobians of various weights for special classes of varieties:
abelian varieties of maximal Picard number, Kummer varieties, and singular K3
surfaces. It turns out that all of these Jacobians are algebraic. We compute
their fields of definition. |
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DOI: | 10.48550/arxiv.2408.12576 |