# Labs septic

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Labs_septic
> Markdown URL: https://mediated.wiki/source/Labs_septic.md
> Source: https://en.wikipedia.org/wiki/Labs_septic
> Source revision: 1356992920
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{Short description|Algebraic surface with 99 nodes}}
In mathematics, the '''Labs septic surface''' is a degree-7 ([septic](/source/Septic_equation)) [nodal surface](/source/nodal_surface) with 99 [nodes](/source/Singular_point_of_an_algebraic_variety) found by {{harvtxt|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 {{harvtxt|Varchenko|1983}}.<ref>The upper bound in degree 7 given by {{harvtxt|Giventalʹ|1983}} is 106.</ref>

thumb|3D model of affine chart of the real Labs septic

==See also==

*[Barth surface](/source/Barth_surface)
*[Endrass surface](/source/Endrass_surface)
*[Sarti surface](/source/Sarti_surface)
*[Togliatti surface](/source/Togliatti_surface)

==References==
{{Reflist}}
*{{citation
 | last = Giventalʹ | first = A. B. | authorlink = Alexander Givental
 | issue = 3
 | journal = Funktsionalʹnyĭ Analiz i ego Prilozheniya
 | mr = 714227
 | pages = 73–74
 | title = The maximum number of singular points on a projective hypersurface
 | volume = 17
 | year = 1983}}
*{{citation|mr=2287352 |arxiv=math/0409348
|last=Labs|first= Oliver
|title=A septic with 99 real nodes
|journal=Rend. Semin. Mat. Univ. Padova|volume= 116 |year=2006|pages= 299–313 |bibcode=2004math......9348L}}
*{{citation
 | last = Varchenko | first = A. N. | authorlink = Alexander Varchenko
 | issue = 6
 | journal = Doklady Akademii Nauk SSSR
 | mr = 712934
 | pages = 1294–1297
 | title = Semicontinuity of the spectrum and an upper bound for the number of singular points of the projective hypersurface
 | volume = 270
 | year = 1983}}

==External links==
*{{citation|url=https://www.youtube.com/watch?v=ufBTEICXKkI|title=video of Labs septic|last=Bothmer|date=4 October 2007 }}

Category:Algebraic surfaces

{{algebraic-geometry-stub}}

---
Adapted from the Wikipedia article [Labs septic](https://en.wikipedia.org/wiki/Labs_septic) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Labs_septic?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.