In algebraic geometry, a Segre surface, studied by txt and txt, is an intersection of two quadrics in 4-dimensional projective space. They are rational surfaces isomorphic to a projective plane blown up in 5 points with no 3 on a line, and are del Pezzo surfaces of degree 4, and have 16 rational lines.

The term "Segre surface" is also occasionally used for various other surfaces, such as a quadric in 3-dimensional projective space (see Segre embedding), or the hypersurface

x_1 x_2 x_3 + x_2 x_3 x_4 + x_3 x_4 x_5 + x_4 x_5 x_1 + x_5 x_1 x_2 = 0. \,

References

  • Segre, Corrado (1884), "Etude des différentes surfaces du 4e ordre à conique double ou cuspidale (générale ou décomposée) considérées comme des projections de l'intersection de deux variétés quadratiques de l'espace à quatre dimensions", Mathematische Annalen. 24: 313–444, Springer Berlin / Heidelberg, doi:10.1007/BF01443412. ISSN 0025-5831
  • Segre, Beniamino (1951), "On the inflexional curve of an algebraic surface in S4", The Quarterly Journal of Mathematics. 2 (1): 216–220, Second Series, doi:10.1093/qmath/2.1.216. ISSN 0033-5606. MR 0044861