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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The Gaussian-Wahl map for trigonal curves

Author: James N. Brawner
Journal: Proc. Amer. Math. Soc. 123 (1995), 1357-1361
MSC: Primary 14H60; Secondary 14N05
MathSciNet review: 1260161
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Abstract: If a curve C is embedded in projective space by a very ample line bundle L, the Gaussian map ${\Phi _{C,L}}$ is defined as the pull-back of hyperplane sections of the classical Gauss map composed with the Plücker 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.

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Article copyright: © Copyright 1995 American Mathematical Society