We show that for every smooth projective hypersurface X ⊂ Pn+1 of degree d and of arbitrary dimension n 2, if X is generic, then there exists a proper algebraic subvariety Y 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 2n5 .
Effective algebraic degeneracy / Diverio, Simone; Merker, J; Rousseau, E.. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - STAMPA. - 180:(2010), pp. 161-223. [10.1007/s00222-010-0232-4]
Effective algebraic degeneracy
DIVERIO, Simone;
2010
Abstract
We show that for every smooth projective hypersurface X ⊂ Pn+1 of degree d and of arbitrary dimension n 2, if X is generic, then there exists a proper algebraic subvariety Y 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 2n5 .File allegati a questo prodotto
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