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arXiv · 2203.06242

On Abel-Jacobi Maps of Lagrangian Families

Chenyu Bai
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Abstract

We study in this article the cohomological properties of Lagrangian families on projective hyper-K\"ahler manifolds. First, we give a criterion for the vanishing of Abel-Jacobi maps of Lagrangian families. Using this criterion, we show that under a natural condition, if the variation of Hodge structures on the degree $1$ cohomomology of the fibers of the Lagrangian family is maximal, its Abel-Jacobi map is trivial. We also construct Lagrangian families on generalized Kummer varieties whose Abel-Jacobi map is not trivial, showing that our criterion is optimal.

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Chenyu Bai. 2022-03-11. On Abel-Jacobi Maps of Lagrangian Families. https://arxiv.org/abs/2203.06242

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