Projective normality of algebraic curves and its application to surfaces

Kim, Seonja; Kim, Young Rock

Osaka J. Math., Tome 44 (2007) no. 1, p. 685-690 / Harvested from Project Euclid

Résumé

Let $L$ be a very ample line bundle on a smooth curve $C$ of genus $g$ with $(3g+3)/2<\deg L\le 2g-5$. Then $L$ is normally generated if $\deg L>\max\{2g+2-4h^1(C,L), 2g-(g-1)/6-2h^1(C,L)\}$. Let $C$ be a triple covering of genus $p$ curve $C'$ with $C\stackrel{\phi}\to C'$ and $D$ a divisor on $C'$ with $4p<\deg D< (g-1)/6-2p$. Then $K_C(-\phi^*D)$ becomes a very ample line bundle which is normally generated. As an application, we characterize some smooth projective surfaces.

Publié le : 2007-09-14
Classification: 14H45, 14H10, 14C20, 14J10, 14J27, 14J28

@article{1189717428,
     author = {Kim, Seonja and Kim, Young Rock},
     title = {Projective normality of algebraic curves and its application to surfaces},
     journal = {Osaka J. Math.},
     volume = {44},
     number = {1},
     year = {2007},
     pages = { 685-690},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1189717428}
}

Kim, Seonja; Kim, Young Rock. Projective normality of algebraic curves and its application to surfaces. Osaka J. Math., Tome 44 (2007) no. 1, pp.  685-690. http://gdmltest.u-ga.fr/item/1189717428/