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Degeneracy of holomorphic curves in surfaces

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Abstract

LetX be a complex projective algebraic manifold of dimension 2 and let D1, ..., Du be distinct irreducible divisors onX such that no three of them share a common point. Let\(f:{\mathbb{C}} \to X\backslash ( \cup _{1 \leqslant i \leqslant u} D_i )\) be a holomorphic map. Assume thatu ⩾ 4 and that there exist positive integers n1, ... ,nu,c such that ninJ D i.Dj) =c for all pairsi,j. Thenf is algebraically degenerate, i.e. its image is contained in an algebraic curve onX.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, 77204, Houston, TX, USA

    Yuancheng Liu & Min Ru

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  1. Yuancheng Liu
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  2. Min Ru
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Correspondence to Yuancheng Liu.

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Liu, Y., Ru, M. Degeneracy of holomorphic curves in surfaces. Sci. China Ser. A-Math. 48 (Suppl 1), 156–167 (2005). https://doi.org/10.1007/BF02884702

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  • DOI: https://doi.org/10.1007/BF02884702

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