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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On genera of smooth curves
in higher dimensional varieties


Author: Jungkai Alfred Chen
Journal: Proc. Amer. Math. Soc. 125 (1997), 2221-2225
MSC (1991): Primary 14H45, 14H99; Secondary 14H50
MathSciNet review: 1401729
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for any smooth projective variety $X$ of dimension $\geq 3$, there exists an integer $g_{0}=g_{0}(X)$, such that for any integer $g \geq g_{0}$, there exists a smooth curve $C$ in $X$ with $g(C) = g$.


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

  • 1. Herbert Clemens, Curves on generic hypersurfaces, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 4, 629–636. MR 875091 (88c:14037)
  • 2. R.Lazarsfeld, Lectures on Linear Series, preprints (1994).

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Additional Information

Jungkai Alfred Chen
Affiliation: Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
Email: jachen@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03908-7
PII: S 0002-9939(97)03908-7
Received by editor(s): February 15, 1996
Communicated by: Ron Donagi
Article copyright: © Copyright 1997 American Mathematical Society