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Transactions of the American Mathematical Society

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Subvarieties of general type on a general projective hypersurface


Author: Gianluca Pacienza
Journal: Trans. Amer. Math. Soc. 356 (2004), 2649-2661
MSC (2000): Primary 14J70, 14K12, 14C99; Secondary 32Q45
DOI: https://doi.org/10.1090/S0002-9947-03-03250-1
Published electronically: October 29, 2003
MathSciNet review: 2052191
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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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Additional Information

Gianluca Pacienza
Affiliation: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4, Place Jussieu, F-75252 Paris Cedex 05, France
Address at time of publication: IRMA - Université Louis Pasteur et CNRS, 7, Rue R. Descartes, 67084 Strasbourg Cedex, France
Email: pacienza@math.jussieu.fr, pacienza@math.u-strasbg.fr

DOI: https://doi.org/10.1090/S0002-9947-03-03250-1
Received by editor(s): August 1, 2002
Received by editor(s) in revised form: October 11, 2002
Published electronically: October 29, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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