The Gaussian-Wahl map for trigonal curves
HTML articles powered by AMS MathViewer
- by James N. Brawner PDF
- Proc. Amer. Math. Soc. 123 (1995), 1357-1361 Request permission
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
-
J. Brawner, The Gaussian map ${\Phi _K}$ for curves with special linear series, Ph.D. dissertation, University of North Carolina, Chapel Hill, 1992.
- Ciro Ciliberto, Joe Harris, and Rick Miranda, On the surjectivity of the Wahl map, Duke Math. J. 57 (1988), no. 3, 829–858. MR 975124, DOI 10.1215/S0012-7094-88-05737-7
- Ciro Ciliberto and Rick Miranda, Gaussian maps for certain families of canonical curves, Complex projective geometry (Trieste, 1989/Bergen, 1989) London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge, 1992, pp. 106–127. MR 1201378, DOI 10.1017/CBO9780511662652.009
- Marc Coppens, The Weierstrass gap sequence of the ordinary ramification points of trigonal coverings of $\textbf {P}^1$; existence of a kind of Weierstrass gap sequence, J. Pure Appl. Algebra 43 (1986), no. 1, 11–25. MR 862870, DOI 10.1016/0022-4049(86)90002-2
- Jeanne Duflot and Rick Miranda, The Gaussian map for rational ruled surfaces, Trans. Amer. Math. Soc. 330 (1992), no. 1, 447–459. MR 1061775, DOI 10.1090/S0002-9947-1992-1061775-4
- Arturo Maroni, Le serie lineari speciali sulle curve trigonali, Ann. Mat. Pura Appl. (4) 25 (1946), 343–354 (Italian). MR 24182, DOI 10.1007/BF02418090
- Jonathan M. Wahl, The Jacobian algebra of a graded Gorenstein singularity, Duke Math. J. 55 (1987), no. 4, 843–871. MR 916123, DOI 10.1215/S0012-7094-87-05540-2
Additional Information
- © Copyright 1995 American Mathematical Society
- 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