Geodesic
Explicit Real Cubic Surfaces
Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 125-133

Voir la notice de l'article provenant de la source Cambridge University Press

The topological classification of smooth real cubic surfaces is recalled and compared to the classification in terms of the number of real lines and of real tritangent planes, as obtained by $\text{L}$ . Schläfli in 1858. Using this, explicit examples of surfaces of every possible type are given.
DOI : 10.4153/CMB-2008-014-5
Mots-clés : 14J25, 14J80, 14P25, 14Q10 
Polo-Blanco, Irene; Top, Jaap. Explicit Real Cubic Surfaces. Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 125-133. doi: 10.4153/CMB-2008-014-5
@article{10_4153_CMB_2008_014_5,
     author = {Polo-Blanco, Irene and Top, Jaap},
     title = {Explicit {Real} {Cubic} {Surfaces}},
     journal = {Canadian mathematical bulletin},
     pages = {125--133},
     year = {2008},
     volume = {51},
     number = {1},
     doi = {10.4153/CMB-2008-014-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-014-5/}
}
TY  - JOUR
AU  - Polo-Blanco, Irene
AU  - Top, Jaap
TI  - Explicit Real Cubic Surfaces
JO  - Canadian mathematical bulletin
PY  - 2008
SP  - 125
EP  - 133
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-014-5/
DO  - 10.4153/CMB-2008-014-5
ID  - 10_4153_CMB_2008_014_5
ER  - 
%0 Journal Article
%A Polo-Blanco, Irene
%A Top, Jaap
%T Explicit Real Cubic Surfaces
%J Canadian mathematical bulletin
%D 2008
%P 125-133
%V 51
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-014-5/
%R 10.4153/CMB-2008-014-5
%F 10_4153_CMB_2008_014_5

[AKP] Artebani, A., Kloosterman, R., and Pacini, M., A new model for the theta divisor of the cubic threefold. Le Matematiche, 58(2003), no. 2, 201–236. Google Scholar

[B] Beauville, A., Complex Algebraic Surfaces. London Mathematical Society Lecture Note Series 68. Cambridge University Press, Cambridge, 1983. Google Scholar

[Cl] Clebsch, A., Ueber die Anwendung der quadratischen Substitution auf die Gleichungen 5ten Grades und die geometrische Theorie des ebenen Fünfseits. Math. Ann. 4(1871), no. 2, 284–345. Google Scholar

[Cr] Cremona, L., Mémoire de géométrie pure sur les surfaces du troisiéme ordre. J. Math Pures Appl. 68(1868), 1–133. Google Scholar

[El] Elkies, N., Complete cubic parametrization of the Fermat cubic surface w 3 + x 3 + y 3 + z 3 = 0. http://www.math.harvard.edu/_elkies/4cubes.html Google Scholar

[F] Fischer, G., ed. Mathematische Modelle, Vieweg, Braunschweig, 1986. Google Scholar

[Ha] Hartshorne, R., Algebraic Geometry. Graduate Texts in Mathematics 52. Springer-Verlag, New York, 1977. Google Scholar

[HL] Holzer, S., and Labs, O., Illustrating the classification of real cubic surfaces. In: Algebraic Geometry and Geometric Modeling. Springer, Berlin, 2006, pp. 119–134. Google Scholar

[Hu] Hunt, B., The Geometry of some special Arithmetic Quotients, Lecture Notes in Mathematics 1637, Springer-Verlag, Berlin, 1996. Google Scholar

[KM] Knörrer, H., and Miller, T., Topologische Typen reeller kubischer Flächen. Math. Z. 195(1987), no. 1, 51–67. Google Scholar

[K] Kollár, J., Real algebraic surfaces, arXiv:AG/9712003, 1997. Google Scholar

[M] Manin, Y. I., Cubic Forms. Second edition. North-Holland, 1974, 1986. Google Scholar

[Po1] Polo-Blanco, I., Mathematical models of surfaces. Inventory, Univ. of Groningen, 2004 http://www.math.rug.nl/models Google Scholar

[Po2] Polo-Blanco, I., Theory and History of Geometric Models. Ph.D. thesis, Groningen, 2007. http://dissertations.ub.rug.nl/faculties/science/2007/i.polo.blanco/. Google Scholar

[Sch] Schläfli, L., An attempt to determine the twenty-seven lines upon a surface of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface, Quart. J. Pure Appl. Math. 2 (1858), 110–120. Google Scholar

[Se] Segre, B., The Non-Singular Cubic Surfaces. Oxford, Oxford University Press, 1942. Google Scholar

[Sh] Shioda, T., Weierstrass transformations and cubic surfaces. Comment. Math. Univ. St. Paul. 44(1995), no. 1, 109–128. Google Scholar

[Si] Silhol, R., Real Algebraic Surfaces, Lecture Notes in Mathematics 1392, Springer-Verlag, Berlin, 1989. Google Scholar

Cité par Sources :