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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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Article copyright: © Copyright 1992 American Mathematical Society

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