Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Rational curves on general projective hypersurfaces


Author: Gianluca Pacienza
Journal: J. Algebraic Geom. 12 (2003), 245-267
DOI: https://doi.org/10.1090/S1056-3911-02-00328-4
Published electronically: October 17, 2002
MathSciNet review: 1949643
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Abstract | References | Additional Information

Abstract: In this article, we study the geometry of $k$-dimensional subvarieties with geometric genus zero of a general projective hypersurface $X_d\subset \mathbf{P}^n$ of degree $d=2n-2-k$, where $k$ is an integer such that $1\leq k\leq n-5$. As a corollary of our main result, we obtain that the only rational curves lying on the general hypersuface $X_{2n-3}\subset \mathbf{P}^n$, for $n\geq 6,$are the lines.


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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: Department of Mathematics, Ohio State University, 100 Mathematics Building, 231 West 18th Avenue, Columbus, Ohio 43210-1174
Email: pacienza@math.jussieu.fr, pacienza@math.ohio-state.edu

DOI: https://doi.org/10.1090/S1056-3911-02-00328-4
Received by editor(s): October 2, 2000
Published electronically: October 17, 2002

American Mathematical Society