Inventiones mathematicae

, Volume 180, Issue 1, pp 161–223 | Cite as

Effective algebraic degeneracy

  • Simone Diverio
  • Joël MerkerEmail author
  • Erwan Rousseau


We show that for every smooth projective hypersurface X⊂ℙn+1 of degree d and of arbitrary dimension n 2, if X is generic, then there exists a proper algebraic subvariety Y X such that every nonconstant entire holomorphic curve f :ℂ→X has image f(ℂ) which lies in Y, as soon as its degree satisfies the effective lower bound \(d\geqslant 2^{n^{5}}\) .


Line Bundle Chern Class Ample Line Bundle Ample Divisor Holomorphic Curf 
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Authors and Affiliations

  1. 1.Istituto “Guido Castelnuovo”Sapienza Università di RomaRomeItaly
  2. 2.Institut de Mathématiques de JussieuUniversité Pierre et Marie CurieParisFrance
  3. 3.Département de Mathématiques et ApplicationsÉcole Normale SupérieureParisFrance
  4. 4.Département de MathématiquesUniversité Louis PasteurStrasbourgFrance

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