Effective algebraic degeneracy

• 成果类型: Article
• 署名作者: Diverio, Simone; Merker, Joel; Rousseau, Erwan
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Sapienza University Rome; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0232-4
• 发表日期: 2010
• 页码: 161-223
• 关键词: projective hypersurfaces; differential-equations; HYPERBOLICITY; CURVES; jets

摘要

We show that for every smooth projective hypersurface X subset of Pn+1 of degree d and of arbitrary dimension n >= 2, if X is generic, then there exists a proper algebraic subvariety Y not subset of 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 >= 2(n5).