On genera of smooth curves in higher dimensional varieties
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- by Jungkai Alfred Chen PDF
- Proc. Amer. Math. Soc. 125 (1997), 2221-2225 Request permission
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
- Herbert Clemens, Curves on generic hypersurfaces, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 4, 629–636. MR 875091
- R.Lazarsfeld, Lectures on Linear Series, preprints (1994).
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
- Received by editor(s): February 15, 1996
- Communicated by: Ron Donagi
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2221-2225
- MSC (1991): Primary 14H45, 14H99; Secondary 14H50
- DOI: https://doi.org/10.1090/S0002-9939-97-03908-7
- MathSciNet review: 1401729