The Gaussian-Wahl Map for Trigonal Curves

If a curve C is embedded in projective space by a very ample line bundle L, the Gaussian map ΦC, Lis defined as the pull-back of hyperplane sections of the classical Gauss map composed with the Plucker embedding. When L = K, the canonical divisor of the curve C, the map is known as the Gaussian-Wahl...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1995-05, Vol.123 (5), p.1357-1361
Main Author: Brawner, James N.
Format: Article
Language:English
Subjects:
Curves
Hyperplanes
Mathematical theorems
Polynomials
Scrolls
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Summary:If a curve C is embedded in projective space by a very ample line bundle L, the Gaussian map ΦC, Lis defined as the pull-back of hyperplane sections of the classical Gauss map composed with the Plucker embedding. When L = K, the canonical divisor of the curve C, the map is known as the Gaussian-Wahl map for C. We determine the corank of the Gaussian-Wahl map to be g + 5 for all trigonal curves (i.e., curves which admit a 3-to-1 mapping onto the projective line) by examining the way in which a trigonal curve is naturally embedded in a rational normal scroll.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1995-1260161-X