Hellenica World

# .

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).

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 714227
Labs, Oliver (2006), "A septic with 99 real nodes", Rend. Sem. Mat. Univ. Padova 116: 299–313, arXiv:math/0409348, 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 712934