Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 10 (2014), 061, 12 pages      arXiv:1310.7150      https://doi.org/10.3842/SIGMA.2014.061
Contribution to the Special Issue on Progress in Twistor Theory

Twistor Topology of the Fermat Cubic

John Armstrong and Simon Salamon
Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK

Received November 06, 2013, in final form May 26, 2014; Published online June 06, 2014

Abstract
We describe topologically the discriminant locus of a smooth cubic surface in the complex projective space ${\mathbb{CP}}^3$ that contains $5$ fibres of the projection ${\mathbb{CP}}^3 \longrightarrow S^4$.

Key words: discriminant locus; Fermat cubic; twistor fibration.

pdf (664 kb)   tex (449 kb)

References

  1. Armstrong J., Povero M., Salamon S., Twistor lines on cubic surfaces, Rend. Semin. Mat. Univ. Politec. Torino, to appear, arXiv:1212.2851.
  2. Atiyah M.F., Geometry of Yang-Mills fields, Scuola Normale Superiore Pisa, Pisa, 1979.
  3. Cayley A., On the triple tangent planes of surfaces of the third order, Cambridge and Dublin Math. J. 4 (1849), 118-138.
  4. Pontecorvo M., Uniformization of conformally flat Hermitian surfaces, Differential Geom. Appl. 2 (1992), 295-305.
  5. Povero M., Modelling Kähler manifolds and projective surfaces, Ph.D. Thesis, Politecnico di Torino, Italy, 2009.
  6. Salamon S., Viaclovsky J., Orthogonal complex structures on domains in ${\mathbb R}^4$, Math. Ann. 343 (2009), 853-899, arXiv:0704.3422v1.
  7. Schläfli L., On the distribution of surfaces of the third order into species, in reference to the absence or presence of singular points, and the reality of their lines, Philos. Trans. Roy. Soc. London 153 (1863), 193-241.

Previous article  Next article   Contents of Volume 10 (2014)