The Gaussian map for rational ruled surfaces
HTML articles powered by AMS MathViewer
- by Jeanne Duflot and Rick Miranda
- Trans. Amer. Math. Soc. 330 (1992), 447-459
- DOI: https://doi.org/10.1090/S0002-9947-1992-1061775-4
- PDF | Request permission
Abstract:
In this paper the Gaussian map $\Phi :{ \wedge ^2}{H^0}(C,K) \to {H^0}(C,3K)$ of a smooth curve $C$ lying on a minimal rational ruled surface is computed. It is shown that the corank of $\Phi$ is determined for almost all such curves by the rational surface in which it lies. Hence, except for some special cases, a curve cannot lie on two nonisomorphic minimal rational ruled surfaces.References
- A. Beauville and J.-Y. Mérindol, Sections hyperplanes des surfaces $K3$, Duke Math. J. 55 (1987), no. 4, 873–878 (French). MR 916124, DOI 10.1215/S0012-7094-87-05541-4
- 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, On the Gaussian map for canonical curves of low genus, Duke Math. J. 61 (1990), no. 2, 417–443. MR 1074304, DOI 10.1215/S0012-7094-90-06118-6 —, Gaussian maps for certain families of canonical curves, Proc. Bergen 1989 Conf. in Algebraic Geometry (to appear).
- Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Rick Miranda, The Gaussian map for certain planar graph curves, Algebraic geometry: Sundance 1988, Contemp. Math., vol. 116, Amer. Math. Soc., Providence, RI, 1991, pp. 115–124. MR 1108635, DOI 10.1090/conm/116/1108635
- B. Saint-Donat, Projective models of $K-3$ surfaces, Amer. J. Math. 96 (1974), 602–639. MR 364263, DOI 10.2307/2373709
- 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 —, Gaussian maps on algebraic curves, Preprint.
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 330 (1992), 447-459
- MSC: Primary 14J26; Secondary 14E25, 14H99
- DOI: https://doi.org/10.1090/S0002-9947-1992-1061775-4
- MathSciNet review: 1061775