Labs septic

In mathematics, the Labs septic surface is a degree-7 (septic) nodal surface with 99 nodes found by Labs (2006). As of 2015, it has the largest known number of nodes of a degree-7 surface, though this number is still less than the best known upper bound of 104 nodes given by Giventalʹ (1983) and Varchenko (1983).

3D model of affine chart of the real Labs septic

See also

• Barth surface
• Endrass surface
• Sarti surface
• Togliatti surface

References

• Giventalʹ, A. B. (1983), "The maximum number of singular points on a projective hypersurface", Funktsionalʹnyĭ Analiz i ego Prilozheniya, 17 (3): 73–74, MR 0714227
• Labs, Oliver (2006), "A septic with 99 real nodes", Rend. Semin. Mat. Univ. Padova, 116: 299–313, arXiv:math/0409348, Bibcode:2004math......9348L, MR 2287352
• Varchenko, A. N. (1983), "Semicontinuity of the spectrum and an upper bound for the number of singular points of the projective hypersurface", Doklady Akademii Nauk SSSR, 270 (6): 1294–1297, MR 0712934

External links

• Bothmer, video of Labs septic