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

DOI:
https://doi.org/10.1090/S0002-9939-1995-1260161-X

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 is defined as the pull-back of hyperplane sections of the classical Gauss map composed with the Plücker embedding. When , 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 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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DOI:
https://doi.org/10.1090/S0002-9939-1995-1260161-X

Article copyright:
© Copyright 1995
American Mathematical Society