## Osaka Journal of Mathematics

### 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 $(3g+3)/2<\deg L\le 2g-5$. 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.

#### Article information

Source
Osaka J. Math., Volume 44, Number 3 (2007), 685-690.

Dates
First available in Project Euclid: 13 September 2007

https://projecteuclid.org/euclid.ojm/1189717428

Mathematical Reviews number (MathSciNet)
MR2360946

Zentralblatt MATH identifier
1127.14028

#### Citation

Kim, Seonja; Kim, Young Rock. Projective normality of algebraic curves and its application to surfaces. Osaka J. Math. 44 (2007), no. 3, 685--690. https://projecteuclid.org/euclid.ojm/1189717428

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