Projective Normality Of Algebraic Curves And Its Application To Surfaces

Details Projective Normality Of Algebraic Curves And Its Application To Surfaces Projective Normality Of Algebraic Curves And Its Application To Surfaces

2006-01-09

arxiv.org/abs/math/0601189v1

Mathematics

Algebraic Geometry

7 pages, 1figure

Scientific paper

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

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