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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the normal generation of ample line bundles on an abelian surface


Author: Akira Ohbuchi
Journal: Proc. Amer. Math. Soc. 117 (1993), 275-277
MSC: Primary 14J25; Secondary 14K05
MathSciNet review: 1106182
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Abstract: Let $ L$ be an ample line bundle on an abelian surface $ A$. We prove that the four conditions: (1) $ L$ is base point free, (2) $ L$ is fixed component free, (3) $ {L^{ \otimes 2}}$ is very ample, (4) $ {L^{ \otimes 2}}$ is normally generated, are equivalent if $ ({L^2}) > 4$. Moreover we prove that $ {L^{ \otimes 2}}$ is not normally generated if $ ({L^2}) = 4$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1106182-7
PII: S 0002-9939(1993)1106182-7
Article copyright: © Copyright 1993 American Mathematical Society