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

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

MathSciNet review:
1061775

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Abstract: In this paper the Gaussian map of a smooth curve lying on a minimal rational ruled surface is computed. It is shown that the corank of 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:
https://doi.org/10.1090/S0002-9947-1992-1061775-4

Article copyright:
© Copyright 1992
American Mathematical Society