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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Gonality and Clifford index of projective curves on ruled surfaces
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by Youngook Choi and Seonja Kim PDF
Proc. Amer. Math. Soc. 140 (2012), 393-402 Request permission

Abstract:

Let $X$ be a smooth curve on a ruled surface $\pi : S\rightarrow C$. In this paper, we deal with the questions on the gonality and the Clifford index of $X$ and on the composedness of line bundles on $X$ with the covering morphism $\pi |_X$. The main theorem shows that if a smooth curve $X\sim aC_o +\textbf {b}f$ satisfies some conditions on the degree of $\bf b$, then a line bundle $\mathcal {L}$ on $X$ with $\mathrm {Cliff}(\mathcal {L})\le ag(C)-1$ is composed with $\pi |_X$. This implies that a part of the gonality sequence of $X$ is computed by the gonality sequence of $C$ as follows: \[ d_r (X)=ad_r (C) ~~\mbox { for }~r\le L,\] where $L$ is the length of the gonality sequence of $C$.
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Additional Information
  • Youngook Choi
  • Affiliation: Department of Mathematics Education, Yeungnam University, 214-1 Daedong Gyeongsan, 712-749, Gyeongsangbuk-do, Republic of Korea
  • MR Author ID: 709698
  • Email: ychoi824@yu.ac.kr
  • Seonja Kim
  • Affiliation: Department of Electronics, Chungwoon University, Hongseong, Chungnam, 350-701, Republic of Korea
  • MR Author ID: 258121
  • Email: sjkim@chungwoon.ac.kr
  • Received by editor(s): September 28, 2009
  • Received by editor(s) in revised form: November 16, 2010
  • Published electronically: June 1, 2011
  • Additional Notes: The first author’s work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00011)
    The second author’s work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (2009-0075469)
  • Communicated by: Bernd Ulrich
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 393-402
  • MSC (2010): Primary 14H51, 14J26, 14H45
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10905-5
  • MathSciNet review: 2846309