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arXiv · 1605.01860

Balanced embedding of degenerating Abelian varieties

Xiaowei Wang·Yuguang Zhang
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Abstract

For a certain maximal unipotent family of Abelian varieties over the punctured disc, we show that after a base change, one can complete the family over a disc such that the whole degeneration can be simultaneously balanced embedded into a projective space by the theta functions. Then we study the relationship between the balanced filling-in and the Gromov-Hausdorff limit of flat K\"{a}hler metrics on the nearby fibers.

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Xiaowei Wang, Yuguang Zhang. 2016-05-06. Balanced embedding of degenerating Abelian varieties. https://arxiv.org/abs/1605.01860

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