Journal of Algebraic Geometry

Author(s): Gianluca Pacienza
Journal: J. Algebraic Geom. 12 (2003), 245-267.
Posted: October 17, 2002
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Abstract: In this article, we study the geometry of

-dimensional subvarieties with geometric genus zero of a general projective hypersurface $X_d\subset \mathbf{P}^n$ of degree

, where

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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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

PII: S 1056-3911(02)00328-4
Received by editor(s): October 2, 2000
Posted: October 17, 2002

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