Gonality and Clifford index of projective curves on ruled surfaces
Authors:
Youngook Choi and Seonja Kim
Journal:
Proc. Amer. Math. Soc. 140 (2012), 393402
MSC (2010):
Primary 14H51, 14J26, 14H45
Published electronically:
June 1, 2011
MathSciNet review:
2846309
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Additional Information
Abstract: Let be a smooth curve on a ruled surface . In this paper, we deal with the questions on the gonality and the Clifford index of and on the composedness of line bundles on with the covering morphism . The main theorem shows that if a smooth curve satisfies some conditions on the degree of , then a line bundle on with is composed with . This implies that a part of the gonality sequence of is computed by the gonality sequence of as follows: for where is the length of the gonality sequence of .
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 Fuentes García, L. and Pedreira, M., The projective theory of ruled surfaces, Note Mat. 24 (1) (2004/2005) 2563. MR 2199622 (2006k:14065)
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Additional Information
Youngook Choi
Affiliation:
Department of Mathematics Education, Yeungnam University, 2141 Daedong Gyeongsan, 712749, Gyeongsangbukdo, Republic of Korea
Email:
ychoi824@yu.ac.kr
Seonja Kim
Affiliation:
Department of Electronics, Chungwoon University, Hongseong, Chungnam, 350701, Republic of Korea
Email:
sjkim@chungwoon.ac.kr
DOI:
http://dx.doi.org/10.1090/S000299392011109055
Keywords:
Gonality,
Clifford index,
ruled surface,
multiple covering,
CastelnuovoSeveri inequality,
gonality sequence.
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 (KRF2008314C00011)
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 (20090075469)
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
