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.

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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 $c:= d-(3g-1)/2$.
Sia $X$ una curva $k$-gonale generale di genere $g$ ed $L \in \text{Pic}^{d}(X)$ con $d:= \text{deg} L > (3g-1)/2$, $h^{1}(X, L)\neq 0$ ed $L$ molto ampio. In questo lavoro dimostriamo che $L$ è normalmente generato se il luogo base di $KL^{-1}$ ha grado al massimo $c(k-2)/2$ con $c:= d-(3g-1)/2$. 
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     title = {Normal generation of line bundles on a general $k$-gonal algebraic curve},
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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/

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