The second main theorem for holomorphic curves into semi-Abelian varieties

By J. Noguchi, J. Winkelmann, K. Yamanoi. 2002

91 citations recorded by the source corpus.

Abstract We establish the second main theorem with the best truncation level one for the k-jet lift Jk (ƒ) : → Jk (A) of an algebraically non-degenerate entire holomorphic curve ƒ : → A into a semi-abelian variety A and an arbitrary algebraic reduced subvariety Z of Jk (A); the low truncation level is important for applications. Finally we give some applications, including the solution of a problem posed by Mark Green (1974). 2000 Mathematics Subject Classification: 32H30.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/40367d8dd375cde5376524384e17213751336ea2

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In Applied Mathematics

1. Y. Siu
2. Damian Brotbek
3. J. Demailly
4. Mihai Paun
5. Qi’an Guan
6. Xiangyu Zhou
7. Joël Merker
8. Junyan Cao

In Computational Theory and Mathematics

1. F. Catanese
2. Ingrid Bauer

In Geometry and Topology

1. Y. Siu
2. J. Demailly
3. Damian Brotbek
4. Qi’an Guan
5. Mihai Paun
6. Xiangyu Zhou
7. Joël Merker
8. Junyan Cao

Citations in the corpus

• Some recent transcendental techniques in algebraic and complex geometry (2002, background): “2 (proved in Addendum of [24]) was added to [24] in response to a difficulty in the proof of Lemma 2 of the original paper [24] pointed out in [13].”
• Degeneracy of holomorphic curves into algebraic varieties (2005, background): “Then the number of A-orbits in X̃ is finite ([20], Lemma 3.12).”