The Gaussian map for rational ruled surfaces
Authors:
Jeanne Duflot and Rick Miranda
Journal:
Trans. Amer. Math. Soc. 330 (1992), 447459
MSC:
Primary 14J26; Secondary 14E25, 14H99
MathSciNet review:
1061775
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: In this paper the Gaussian map of a smooth curve lying on a minimal rational ruled surface is computed. It is shown that the corank of 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.
 [BM]
A.
Beauville and J.Y.
Mérindol, Sections hyperplanes des surfaces 𝐾3,
Duke Math. J. 55 (1987), no. 4, 873–878
(French). MR
916124 (89a:14043), http://dx.doi.org/10.1215/S0012709487055414
 [CHM]
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
(89m:14010), http://dx.doi.org/10.1215/S0012709488057377
 [CM1]
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
(91i:14018), http://dx.doi.org/10.1215/S0012709490061186
 [CM2]
, Gaussian maps for certain families of canonical curves, Proc. Bergen 1989 Conf. in Algebraic Geometry (to appear).
 [GH]
Phillip
Griffiths and Joseph
Harris, Principles of algebraic geometry, WileyInterscience
[John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR 507725
(80b:14001)
 [H]
Robin
Hartshorne, Algebraic geometry, SpringerVerlag, New York,
1977. Graduate Texts in Mathematics, No. 52. MR 0463157
(57 #3116)
 [M]
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
(92h:14016), http://dx.doi.org/10.1090/conm/116/1108635
 [SD]
B.
SaintDonat, Projective models of 𝐾3 surfaces, Amer.
J. Math. 96 (1974), 602–639. MR 0364263
(51 #518)
 [W1]
Jonathan
M. Wahl, The Jacobian algebra of a graded Gorenstein
singularity, Duke Math. J. 55 (1987), no. 4,
843–871. MR
916123 (89a:14042), http://dx.doi.org/10.1215/S0012709487055402
 [W2]
, Gaussian maps on algebraic curves, Preprint.
 [BM]
 A. Beauville and J.Y. Mérindol, Sections hyperplanes des surfaces , Duke. Math. J. 55 (1987), 873878. MR 916124 (89a:14043)
 [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)
 [CM1]
 C. Ciliberto and R. Miranda, On the Gaussian map for canonical curves of low genus, Duke Math. J. 61 (1990), 417443. MR 1074304 (91i:14018)
 [CM2]
 , Gaussian maps for certain families of canonical curves, Proc. Bergen 1989 Conf. in Algebraic Geometry (to appear).
 [GH]
 P. A. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York, 1978. MR 507725 (80b:14001)
 [H]
 R. Hartshorne, Algebraic geometry, Graduate Texts in Math., Vol. 52, SpringerVerlag, New York, 1977. MR 0463157 (57:3116)
 [M]
 R. Miranda, On the Wahl map for certain planar graph curves, (B. Harbourne and R. Speiser, eds.), Algebraic Geometry: Sundance 1988, Contemp. Math., vol. 116, Amer. Math. Soc., Providence, R.I., 1991, pp. 115124. MR 1108635 (92h:14016)
 [SD]
 B. SaintDonat, Projective models of surfaces, Amer. J. Math. 96 (1974), 602639. MR 0364263 (51:518)
 [W1]
 J. Wahl, On the Jacobian algebra of a graded Gorenstein singularity, Duke Math. J. 55 (1987), 843871. MR 916123 (89a:14042)
 [W2]
 , Gaussian maps on algebraic curves, Preprint.
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC:
14J26,
14E25,
14H99
Retrieve articles in all journals
with MSC:
14J26,
14E25,
14H99
Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199210617754
PII:
S 00029947(1992)10617754
Article copyright:
© Copyright 1992 American Mathematical Society
