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Projective normality of ruled surfaces

Author(s): Euisung Park
Journal: Proc. Amer. Math. Soc. 136 (2008), 839-847.
MSC (2000): Primary 14J26
Posted: November 30, 2007
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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$   Pic$ X$ with deg$ (L) \geq 2g+1-2h^1 (X,L) -$   Cliff$ (X)$ is normally generated where 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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Additional Information:

Euisung Park
Affiliation: Department of Mathematics, Korea University, Seoul 136-701, Republic of Korea
Email: euisungpark@korea.ac.kr

DOI: 10.1090/S0002-9939-07-09121-6
PII: S 0002-9939(07)09121-6
Received by editor(s): July 15, 2005
Received by editor(s) in revised form: February 19, 2007
Posted: November 30, 2007
Communicated by: Michael Stillman
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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