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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The Gaussian map for rational ruled surfaces


Authors: Jeanne Duflot and Rick Miranda
Journal: Trans. Amer. Math. Soc. 330 (1992), 447-459
MSC: Primary 14J26; Secondary 14E25, 14H99
MathSciNet review: 1061775
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Abstract: In this paper the Gaussian map $ \Phi :{ \wedge ^2}{H^0}(C,K) \to {H^0}(C,3K)$ of a smooth curve $ C$ lying on a minimal rational ruled surface is computed. It is shown that the corank of $ \Phi $ is determined for almost all such curves by the rational surface in which it lies. Hence, except for some special cases, a curve cannot lie on two nonisomorphic minimal rational ruled surfaces.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1061775-4
PII: S 0002-9947(1992)1061775-4
Article copyright: © Copyright 1992 American Mathematical Society