We show that for every smooth generic projective hypersurface X in P^{n+1} there exists a proper subvariety Y in X of codimension at least 2 such that for every non-constant holomorphic map f: C--->X one has f(C) is contained in Y, provided that the degree of X is greater than 2^{n^5}. In particular we obtain an affirmative confirmation of the Kobayashi conjecture for threefolds in P^4.
Diverio, S., Trapani, S. (2010). A remark on the codimension of the Green-Griffiths locus of generic projective hypersurfaces of high degree. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 2010(649), 55-61 [10.1515/CRELLE.2010.088].
A remark on the codimension of the Green-Griffiths locus of generic projective hypersurfaces of high degree.
TRAPANI, STEFANO
2010-01-01
Abstract
We show that for every smooth generic projective hypersurface X in P^{n+1} there exists a proper subvariety Y in X of codimension at least 2 such that for every non-constant holomorphic map f: C--->X one has f(C) is contained in Y, provided that the degree of X is greater than 2^{n^5}. In particular we obtain an affirmative confirmation of the Kobayashi conjecture for threefolds in P^4.File in questo prodotto:
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