Subvarieties of general type on a general projective hypersurface

Pacienza, Gianluca

doi:10.1090/S0002-9947-03-03250-1

Subvarieties of general type on a general projective hypersurface
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by Gianluca Pacienza PDF

Trans. Amer. Math. Soc. 356 (2004), 2649-2661 Request permission

Abstract:

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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