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# 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).

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 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

External links

Bothmer, video of Labs septic

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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