Double covering of curves
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- by Edoardo Ballico, Changho Keem and Seungsuk Park PDF
- Proc. Amer. Math. Soc. 132 (2004), 3153-3158 Request permission
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 $g\ge 4q+5$).References
- E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of algebraic curves. Vol. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 267, Springer-Verlag, New York, 1985. MR 770932, DOI 10.1007/978-1-4757-5323-3
- Edoardo Ballico and Changho Keem, On multiple coverings of irrational curves, Arch. Math. (Basel) 65 (1995), no. 2, 151–160. MR 1338248, DOI 10.1007/BF01270694
- Edoardo Ballico and Changho Keem, Variety of linear systems on double covering curves, J. Pure Appl. Algebra 128 (1998), no. 3, 213–224. MR 1626341, DOI 10.1016/S0022-4049(97)00057-1
- Ernst Kani, On Castelnuovo’s equivalence defect, J. Reine Angew. Math. 352 (1984), 24–70. MR 758693, DOI 10.1515/crll.1984.352.24
- Igor Reider, Vector bundles of rank $2$ and linear systems on algebraic surfaces, Ann. of Math. (2) 127 (1988), no. 2, 309–316. MR 932299, DOI 10.2307/2007055
- N. I. Shepherd-Barron, Unstable vector bundles and linear systems on surfaces in characteristic $p$, Invent. Math. 106 (1991), no. 2, 243–262. MR 1128214, DOI 10.1007/BF01243912
Additional Information
- Edoardo Ballico
- Affiliation: Department of Mathematics, Università di Trento, 38050 Povo(TN), Italy
- MR Author ID: 30125
- 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
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3153-3158
- MSC (2000): Primary 14H51, 14H30
- DOI: https://doi.org/10.1090/S0002-9939-04-07426-X
- MathSciNet review: 2073288