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An inequality of Clifford indices for a finite covering of curves. (English) Zbl 1073.14528

Summary: We prove that for a finite covering of curves the Clifford index of the source is at least that of the target.

MSC:

14H30 Coverings of curves, fundamental group
14H51 Special divisors on curves (gonality, Brill-Noether theory)
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References:

[1] [ACGH] E. Arbarello, M. Cornalba, P. A. Griffiths and J. Harris,Geometry of algebraic curves Vol. 1, Grundlehren Math. Wiss.267: (1985), Springer-Verlag.
[2] [CM] M. Coppens and G. Martens,Secant spaces and Clifford’s theorem, Composition Math.78: (1991), 193-212. · Zbl 0741.14035
[3] [M] H. H. Martens,Varieties of special divisors on a curve II, J. Reine Angew Math.233: (1968), 89-100. · Zbl 0221.14004 · doi:10.1515/crll.1968.233.89
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