On holomorphic curves in semi-Abelian varieties (Q1273146)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On holomorphic curves in semi-Abelian varieties |
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On holomorphic curves in semi-Abelian varieties (English)
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8 March 1999
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Let \(A\) be a complex semi-abelian variety, let \(D\) be an algebraic hypersurface in \(A\) and let \(f:{\mathbb C}\to A\setminus D\) be a holomorphic mapping. The purpose of this article is to prove a conjecture of Lang: The Zariski closure of the image of \(f\) is a translate of a semi-abelian variety which does not meet \(D\). The conjecture was proved by \textit{Y.-T. Siu} and \textit{S.-K. Yeung} [Math. Ann. 306, No. 4, 743-758 (1996; Zbl 0882.32009)] when \(A\) is an abelian variety and the proof presented here is an elaboration and simplification of their arguments using infinite order jet spaces over jet spaces.
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algebraic hypersurface
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semi-abelian varieties
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Lang conjecture
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jet spaces
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