Projective normality of ruled surfaces

Park, Euisung

doi:10.1090/S0002-9939-07-09121-6

Projective normality of ruled surfaces
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Proc. Amer. Math. Soc. 136 (2008), 839-847 Request permission

Abstract:

In this article we study normal generation of irrational ruled surfaces. When $C$ is a smooth curve of genus $g$, Green and Lazarsfeld proved that a very ample line bundle $L \in \mbox {Pic}X$ with $\mbox {deg}(L) \geq 2g+1-2h^1 (X,L) - \mbox {Cliff}(X)$ is normally generated where $\mbox {Cliff}(C)$ denotes the Clifford index of the curve $C$ (Green and Lazarsfeld, 1986). We generalize this to line bundles on a ruled surface over $C$.

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