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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Families of singular rational curves

Author: Stefan Kebekus
Journal: J. Algebraic Geom. 11 (2002), 245-256
Published electronically: November 27, 2001
MathSciNet review: 1874114
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Abstract | References | Additional Information

Abstract: Let $X$ be a projective variety which is covered by a family of rational curves of minimal degrees. We give a bound on the dimension of the subfamily of singular rational curves. Among other applications, we will show that this yields a new characterization of the projective space in terms of rational curves.

References [Enhancements On Off] (What's this?)

    [CMS00]CMS00 K. Cho, Y. Miyaoka and N.I. Shepherd-Barron. Characterizations of Projective Space and Applications to Complex Symplectic Manifolds. unpublished preprint, 2000. [CS95]CS95 K. Cho and E. Sato. Smooth projective varieties with ample vector bundle $\bigwedge ^2 T_X$ in any characteristic. J. Math. Kyoto Univ., 35:1–33, 1995. [Keb00]Keb00 S. Kebekus. Projective bundles of singular plane cubics. preprint math.AG/ 0009083, 2000, to appear in Math. Nachr. [KO73]KO73 S. Kobayashi and T. Ochiai. Characterizations of complex projective spaces and hyperquadrics. J. Math. Kyoto Univ., 13:31–47, 1973. [Kol96]K96 J. Kollár. Rational Curves on Algebraic Varieties, volume 32 of Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge. Springer, 1996. [KS99]KS99 Y. Kachi and E. Sato. Polarized varieties whose points are joined by rational curves of small degrees. Illinois J. Math., 43(2):350–390, 1999.

Additional Information

Stefan Kebekus
Affiliation: Institut für Mathematik, Universität Bayreuth, 95440 Bayreuth, Germany
MR Author ID: 637173

Received by editor(s): June 5, 2000
Published electronically: November 27, 2001
Additional Notes: The author gratefully acknowledges support by a Forschungs- stipendium of the Deutsche Forschungsgemeinschaft.