Subvarieties of general type on a general projective hypersurface
Abstract
Description
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.
Title changed, introduction completely rewritten, exposition improved. To appear in the Transactions of the A.M.S. 18 pages, Latex
Title changed, introduction completely rewritten, exposition improved. To appear in the Transactions of the A.M.S. 18 pages, Latex