Rational curves on general projective hypersurfaces
Author:
Gianluca Pacienza
Journal:
J. Algebraic Geom. 12 (2003), 245267
DOI:
https://doi.org/10.1090/S1056391102003284
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 $d=2n2k$, where $k$ is an integer such that $1\leq k\leq n5$. As a corollary of our main result, we obtain that the only rational curves lying on the general hypersuface $X_{2n3}\subset \mathbf {P}^n$, 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, F75252 Paris CEDEX 05  FRANCE
Address at time of publication:
Department of Mathematics, Ohio State University, 100 Mathematics Building, 231 West 18th Avenue, Columbus, Ohio 432101174
Email:
pacienza@math.jussieu.fr, pacienza@math.ohiostate.edu
Received by editor(s):
October 2, 2000
Published electronically:
October 17, 2002