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

 

Double covering of curves


Authors: Edoardo Ballico, Changho Keem and Seungsuk Park
Journal: Proc. Amer. Math. Soc. 132 (2004), 3153-3158
MSC (2000): Primary 14H51, 14H30
Published electronically: May 12, 2004
MathSciNet review: 2073288
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Abstract: Let $C$ be a smooth projective algebraic curve of genus $q$ and $g$ an integer with $g\ge 4q+5$. For all integers $d\ge g-2q+1$ we prove the existence of a double covering $f:X\to C$with $X$ a smooth curve of genus $g$ and the existence of a degree $d$ morphism $u:X\to \mathbb P^1$ that does not factor through $f$. By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound $g\ge 4q+5$).


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Additional Information

Edoardo Ballico
Affiliation: Department of Mathematics, Università di Trento, 38050 Povo(TN), Italy
Email: ballico@science.unitn.it

Changho Keem
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, South Korea
Email: ckeem@math.snu.ac.kr

Seungsuk Park
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, South Korea
Address at time of publication: Mathematics Section, The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy
Email: s2park@math.snu.ac.kr, spark@ictp.trieste.it

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07426-X
PII: S 0002-9939(04)07426-X
Keywords: Double coverings, base-point-free pencil, Castelnuovo-Severi inequality, Brill-Noether theory
Received by editor(s): January 15, 2001
Received by editor(s) in revised form: July 7, 2003
Published electronically: May 12, 2004
Additional Notes: The first named author was partially supported by MIUR and GNSAGA of INdAM (Italy). The second named author was supported by Korea Research Foundation Grant #2001-015-DS0003.
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society