Projective Normality Of Algebraic Curves And Its Application To Surfaces
Abstract
Let $L$ be a very ample line bundle on a smooth curve $C$ of genus $g$ with $\frac{3g+3}{2}<°L\le 2g5$. Then $L$ is normally generated if $°L>\max\{2g+24h^1(C,L), 2g\frac{g1}{6}2h^1(C,L)\}$. Let $C$ be a triple covering of genus $p$ curve $C'$ with $C\stackrel{\phi}\to C'$ and $D$ a divisor on $C'$ with $4p<°D< \frac{g1}{6}2p$. Then $K_C(\phi^*D)$ becomes a very ample line bundle which is normally generated. As an application, we characterize some smooth projective surfaces.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2006
 arXiv:
 arXiv:math/0601189
 Bibcode:
 2006math......1189K
 Keywords:

 Mathematics  Algebraic Geometry;
 14H45;
 14H10;
 14C20;
 14J10;
 14J27;
 14J28
 EPrint:
 7 pages, 1figure