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}
}