Science in China Series A: Mathematics

, Volume 48, Issue 1, pp 156-167

First online:

Degeneracy of holomorphic curves in surfaces

  • Yuancheng LiuAffiliated withDepartment of Mathematics, University of Houston Email author 
  • , Min RuAffiliated withDepartment of Mathematics, University of Houston

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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.


degeneracy of holomorphic curves Nevanlinna theory complex projective surface second main theorem