Geodesic
Normal generation of line bundles on a general $k$-gonal algebraic curve
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 557-562 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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We prove that a very ample special line bundle $L$ of degree $d>(3g-1)/2$ on a general $k$-gonal curve is normally generated if the degree of the base locus of its dual bundle $KL^{-1}$ does not exceed $c(k-2)/2$, where $c:= d-(3g-1)/2$. 
@article{BUMI_2003_8_6B_3_a3,
     author = {Ballico, Edoardo and Keem, Changho and Kim, Seonja},
     title = {Normal generation of line bundles on a general $k$-gonal algebraic curve},
     journal = {Bollettino della Unione matematica italiana},
     pages = {557--562},
     year = {2003},
     volume = {Ser. 8, 6B},
     number = {3},
     zbl = {1178.14030},
     mrnumber = {MR2014818},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a3/}
}
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Ballico, Edoardo; Keem, Changho; Kim, Seonja. Normal generation of line bundles on a general $k$-gonal algebraic curve. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 557-562. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a3/