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January, 2019 Pseudo Kobayashi hyperbolicity of subvarieties of general type on abelian varieties
Katsutoshi YAMANOI
J. Math. Soc. Japan 71(1): 259-298 (January, 2019). DOI: 10.2969/jmsj/75817581

Abstract

We prove that the Kobayashi pseudo distance of a closed subvariety $X$ of an abelian variety $A$ is a true distance outside the special set $\operatorname{Sp}(X)$ of $X$, where $\operatorname{Sp}(X)$ is the union of all positive dimensional translated abelian subvarieties of $A$ which are contained in $X$. More strongly, we prove that a closed subvariety $X$ of an abelian variety is taut modulo $\operatorname{Sp}(X)$; Every sequence $f_n:{\mathbb{D}}\to X$ of holomorphic mappings from the unit disc ${\mathbb{D}}$ admits a subsequence which converges locally uniformly, unless the image $f_n(K)$ of a fixed compact set $K$ of ${\mathbb{D}}$ eventually gets arbitrarily close to $\operatorname{Sp}(X)$ as $n$ gets larger. These generalize a classical theorem on algebraic degeneracy of entire curves in irregular varieties.

Funding Statement

The author was supported by JSPS Grant-in-Aid for Scientific Research (C), 24540069 and by JSPS Grant-in-Aid for Scientific Research (B), 17H02842.

Citation

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Katsutoshi YAMANOI. "Pseudo Kobayashi hyperbolicity of subvarieties of general type on abelian varieties." J. Math. Soc. Japan 71 (1) 259 - 298, January, 2019. https://doi.org/10.2969/jmsj/75817581

Information

Received: 10 August 2016; Revised: 17 August 2017; Published: January, 2019
First available in Project Euclid: 20 November 2018

zbMATH: 07056564
MathSciNet: MR3909921
Digital Object Identifier: 10.2969/jmsj/75817581

Subjects:
Primary: 32Q45
Secondary: 14K12 , 32H30

Keywords: Nevanlinna theory , pseudo Kobayashi hyperbolicity , tautness

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 1 • January, 2019
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