Effective algebraic degeneracy
Abstract
We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = Xn in Pn+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.
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