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On the Clifford index of a general \((e+2)\)-gonal curve. (English) Zbl 0679.14015
The authors give an alternative proof of a theorem of Ballico: a general \((e+2)\)-gonal curve of genus \(g\geq 2e+2\) has \(Clifford\quad index\quad e.\) They use a result of E. Arbarello and M. Cornalba [Ann. Sci. Éc. Norm. Supér., IV. Sér. 16, 467-488 (1983; Zbl 0553.14009)] to provide a lemma for the theorem. The lemma gives an upper bound on the dimension of the variety of special linear systems on a variable curve.
As to the reverse of the theorem see H. M. Farkas, J. Reine Angew. Math. 391, 213-220 (1988; Zbl 0651.14018).
Reviewer: R.Horiuchi

MSC:
14H45 Special algebraic curves and curves of low genus
14C20 Divisors, linear systems, invertible sheaves
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References:
[1] E. Arbarello, M. Cornalba, ?A few remarks about the variety of irreducible plane curves of given degree and genus?, Ann.scient. Éc. Norm. Sup., 4e serie, t.16 (1983), 467-483 · Zbl 0553.14009
[2] E. Ballico, ?On the Clifford index of algebraic curves?, Proc. of the Amer. Math. Soc., 97(1986), 217-218 · Zbl 0591.14020
[3] M. Green, R. Lazarsfeld, ?On the projective normality of complete linear series on an algebraic curve?, Invent. math. 83(1986), 73-90 · Zbl 0594.14010
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