The Gaussian map for rational ruled surfaces

Duflot, Jeanne; Miranda, Rick

doi:10.1090/S0002-9947-1992-1061775-4

The Gaussian map for rational ruled surfaces
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by Jeanne Duflot and Rick Miranda

Trans. Amer. Math. Soc. 330 (1992), 447-459

DOI: https://doi.org/10.1090/S0002-9947-1992-1061775-4

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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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Gaussian maps on algebraic curves