Balanced embedding of degenerating Abelian varieties

10 May 2016  ·  Wang Xiaowei, Zhang Yuguang ·

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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Algebraic Geometry Differential Geometry