Normal generation of line bundles on a general $k$-gonal algebraic curve

Ballico, Edoardo; Keem, Changho; Kim, Seonja

Normal generation of line bundles on a general

k

-gonal algebraic curve

Ballico, Edoardo ; Keem, Changho ; Kim, Seonja

Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003), p. 557-562 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

We prove that a very ample special line bundle $L$ of degree $d > (3 g - 1) / 2$ on a general $k$ -gonal curve is normally generated if the degree of the base locus of its dual bundle $K L^{- 1}$ does not exceed $c (k - 2) / 2$ , where $c := d - (3 g - 1) / 2$ .

Sia $X$ una curva $k$ -gonale generale di genere $g$ ed $L \in {Pic}^{d} (X)$ con $d := deg L > (3 g - 1) / 2$ , $h^{1} (X, L) \neq 0$ ed $L$ molto ampio. In questo lavoro dimostriamo che $L$ è normalmente generato se il luogo base di $K L^{- 1}$ ha grado al massimo $c (k - 2) / 2$ con $c := d - (3 g - 1) / 2$ .

Publié le : 2003-10-01

MR 2014818 | Zbl 1178.14030

@article{BUMI_2003_8_6B_3_557_0,
     author = {Edoardo Ballico and Changho Keem and Seonja Kim},
     title = {Normal generation of line bundles on a general $k$-gonal algebraic curve},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {6-A},
     year = {2003},
     pages = {557-562},
     zbl = {1178.14030},
     mrnumber = {2014818},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2003_8_6B_3_557_0}
}

Ballico, Edoardo; Keem, Changho; Kim, Seonja. Normal generation of line bundles on a general $k$-gonal algebraic curve. Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003) pp. 557-562. http://gdmltest.u-ga.fr/item/BUMI_2003_8_6B_3_557_0/

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