The GaussianWahl map for trigonal curves
Author:
James N. Brawner
Journal:
Proc. Amer. Math. Soc. 123 (1995), 13571361
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 is defined as the pullback 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 GaussianWahl map for C. We determine the corank of the GaussianWahl map to be for all trigonal curves (i.e., curves which admit a 3to1 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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J. Brawner, The Gaussian map for curves with special linear series, Ph.D. dissertation, University of North Carolina, Chapel Hill, 1992.
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 J. Brawner, The Gaussian map for curves with special linear series, Ph.D. dissertation, University of North Carolina, Chapel Hill, 1992.
 [CHM]
 C. Ciliberto, J. Harris, and R. Miranda, On the surjectivity of the Wahl map, Duke Math. J. 57 (1988), 829858. MR 975124 (89m:14010)
 [CM]
 C. Ciliberto and R. Miranda, Gaussian maps for certain families of canonical curves, Complex Projective Geometry (G. Ellingsrud et al., eds.), London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge and New York, 1992, pp. 106127. MR 1201378 (93m:14028)
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 M. Coppens, The Weierstrass gap sequences of the ordinary ramification points of trigonal coverings of ; Existence of a kind of Weierstrass gap sequence, J. Pure Appl. Algebra 43 (1986), 1125. MR 862870 (87j:14049)
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 J. Duflot and R. Miranda, The Gaussian map for rational ruled surfaces, Trans. Amer. Math. Soc. 330 (1992), 447459. MR 1061775 (92f:14030)
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 A. Maroni, Le serie lineari sulle curve trigonali, Ann. Mat. Pura Appl. 25 (1946), 341354. MR 0024182 (9:463j)
 [Wa]
 J. Wahl, The Jacobian algebra of a graded Gorenstein singularity, Duke Math. J. 55 (1987), 843871. MR 916123 (89a:14042)
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DOI:
http://dx.doi.org/10.1090/S0002993919951260161X
PII:
S 00029939(1995)1260161X
Article copyright:
© Copyright 1995
American Mathematical Society
