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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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).
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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
  • 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