Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1995-1260161-X
MathSciNet review: 1260161
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [Br] J. Brawner, The Gaussian map $ {\Phi _K}$ 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), 829-858. 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. 106-127. MR 1201378 (93m:14028)
  • [Co] M. Coppens, The Weierstrass gap sequences of the ordinary ramification points of trigonal coverings of $ {{\mathbf{P}}^1}$; Existence of a kind of Weierstrass gap sequence, J. Pure Appl. Algebra 43 (1986), 11-25. MR 862870 (87j:14049)
  • [DM] J. Duflot and R. Miranda, The Gaussian map for rational ruled surfaces, Trans. Amer. Math. Soc. 330 (1992), 447-459. MR 1061775 (92f:14030)
  • [Ma] A. Maroni, Le serie lineari sulle curve trigonali, Ann. Mat. Pura Appl. 25 (1946), 341-354. MR 0024182 (9:463j)
  • [Wa] J. Wahl, The Jacobian algebra of a graded Gorenstein singularity, Duke Math. J. 55 (1987), 843-871. MR 916123 (89a:14042)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14H60, 14N05

Retrieve articles in all journals with MSC: 14H60, 14N05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1260161-X
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society