Effective algebraic degeneracy

Abstract

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}.

References in corpus (1)

• Differential Equations on Complex Projective Hypersurfaces of Low Dimension

Cited by in corpus (9)

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• Construction of hyperbolic hypersurfaces of low degree in $p^n(c)$
• Hyperbolicity of cyclic covers and complements
• Entire curves producing distinct Nevanlinna currents
• Effective bounds on ampleness of cotangent bundles
• On the Gauss maps of complete minimal surfaces in ${\mathbb{R}}^n$