Effective algebraic degeneracy

Details Effective algebraic degeneracy Effective algebraic degeneracy

2008-11-14

arxiv.org/abs/0811.2346v6

Invent. Math. 180 (2010), 161-223.

Mathematics

Algebraic Geometry

Scientific paper

10.1007/s00222-010-0232-4

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}}.

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