English

Balanced embedding of degenerating Abelian varieties

Algebraic Geometry 2016-05-11 v2 Differential Geometry

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.

Keywords

Cite

@article{arxiv.1605.01860,
  title  = {Balanced embedding of degenerating Abelian varieties},
  author = {Xiaowei Wang and Yuguang Zhang},
  journal= {arXiv preprint arXiv:1605.01860},
  year   = {2016}
}