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Balanced embedding of degenerating Abelian varieties (1605.01860v2)
Published 6 May 2016 in math.AG and math.DG
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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