Abstract
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.
Citation
Seonja Kim. Young Rock Kim. "Projective normality of algebraic curves and its application to surfaces." Osaka J. Math. 44 (3) 685 - 690, September 2007.
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