Osaka Journal of Mathematics

Projective normality of algebraic curves and its application to surfaces

Seonja Kim and Young Rock Kim

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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

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

First available in Project Euclid: 13 September 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H45: Special curves and curves of low genus 14H10: Families, moduli (algebraic) 14C20: Divisors, linear systems, invertible sheaves 14J10: Families, moduli, classification: algebraic theory 14J27: Elliptic surfaces 14J28: $K3$ surfaces and Enriques surfaces


Kim, Seonja; Kim, Young Rock. Projective normality of algebraic curves and its application to surfaces. Osaka J. Math. 44 (2007), no. 3, 685--690.

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