Balanced embedding of degenerating Abelian varieties

Xiaowei Wang; Yuguang Zhang

doi:10.1090/pspum/096/01653

Balanced embedding of degenerating Abelian varieties

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

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 Kähler metrics on the nearby fibers.

Original language	English
Title of host publication	String-Math 2015, Proc. Sympos. Pure Math., 96, Amer. Math. Soc.
Editors	Wei Song, Bong H. Lian, Si Li, Shing-Tung Yau
Publisher	American Mathematical Society
Pages	247-263
Number of pages	17
ISBN (Electronic)	9781470442767
ISBN (Print)	9781470429515
DOIs	https://doi.org/10.1090/pspum/096/01653
Publication status	Published - 2017
Externally published	Yes
Event	proceedings of the conference String-Math, 2015 - Sanya, China Duration: 31 Dec 2015 → 4 Jan 2016

Publication series

Name	Proceedings of Symposia in Pure Mathematics
Volume	96
ISSN (Print)	0082-0717

Conference

Conference	proceedings of the conference String-Math, 2015
Country/Territory	China
City	Sanya
Period	31/12/15 → 4/01/16

Keywords

Abelian variety
Balanced embedding
Theta function

Access to Document

10.1090/pspum/096/01653

Cite this

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title = "Balanced embedding of degenerating Abelian varieties",

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 = "Abelian variety, Balanced embedding, Theta function",

author = "Xiaowei Wang and Yuguang Zhang",

note = "Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.; proceedings of the conference String-Math, 2015 ; Conference date: 31-12-2015 Through 04-01-2016",

year = "2017",

doi = "10.1090/pspum/096/01653",

language = "English",

isbn = "9781470429515",

series = "Proceedings of Symposia in Pure Mathematics",

publisher = "American Mathematical Society",

pages = "247--263",

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booktitle = "String-Math 2015, Proc. Sympos. Pure Math., 96, Amer. Math. Soc.",

}

Wang, X & Zhang, Y 2017, Balanced embedding of degenerating Abelian varieties. in W Song, BH Lian, S Li & S-T Yau (eds), String-Math 2015, Proc. Sympos. Pure Math., 96, Amer. Math. Soc.. Proceedings of Symposia in Pure Mathematics, vol. 96, American Mathematical Society, pp. 247-263, proceedings of the conference String-Math, 2015, Sanya, China, 31/12/15. https://doi.org/10.1090/pspum/096/01653

Balanced embedding of degenerating Abelian varieties. / Wang, Xiaowei; Zhang, Yuguang.
String-Math 2015, Proc. Sympos. Pure Math., 96, Amer. Math. Soc.. ed. / Wei Song; Bong H. Lian; Si Li; Shing-Tung Yau. American Mathematical Society, 2017. p. 247-263 (Proceedings of Symposia in Pure Mathematics; Vol. 96).

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

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KW - Theta function

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Balanced embedding of degenerating Abelian varieties

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Keywords

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