Effective algebraic degeneracy
Algebraic Geometry
2017-04-04 v6 Complex Variables
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}}.
Cite
@article{arxiv.0811.2346,
title = {Effective algebraic degeneracy},
author = {Simone Diverio and Joel Merker and Erwan Rousseau},
journal= {arXiv preprint arXiv:0811.2346},
year = {2017}
}