Subvarieties of general type on a general projective hypersurface

Details Subvarieties of general type on a general projective hypersurface Subvarieties of general type on a general projective hypersurface

2002-04-24

arxiv.org/abs/math/0204297v2

Mathematics

Algebraic Geometry

Title changed, introduction completely rewritten, exposition improved. To appear in the Transactions of the A.M.S. 18 pages, L

Scientific paper

We study subvarieties of a general projective degree $d$ hypersurface
$X_d\subset \mathbf P^n$. Our main theorem, which improves previous results of
L. Ein and C. Voisin, implies in particular the following sharp corollary: any
subvariety of a general hypersurface $X_{d}\subset {\mathbf P}^n$, for $n\geq
6$ and $d\geq 2n-2$, is of general type.

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