@prefix psr: . @prefix skos: . @prefix dc: . @prefix xsd: . psr:-K7V5TJHT-T skos:broader psr:-HT4QK75C-T, psr:-QP0D47D3-D ; skos:altLabel "Bring's surface"@en, "surface de Bring"@fr ; dc:modified "2024-10-18"^^xsd:date ; skos:exactMatch ; skos:inScheme psr: ; skos:definition """In mathematics, Bring's curve (also called Bring's surface and, by analogy with the Klein quartic, the Bring sextic) is the curve in

{\\\\displaystyle \\\\mathbb {P} ^{4}}

cut out by the homogeneous equations

{\\\\displaystyle v+w+x+y+z=v^{2}+w^{2}+x^{2}+y^{2}+z^{2}=v^{3}+w^{3}+x^{3}+y^{3}+z^{3}=0.}

It was named by Klein (2003, p.157) after Erland Samuel Bring who studied a similar construction in 1786 in a Promotionschrift submitted to the University of Lund. Note that the roots x_i of the Bring quintic

{\\\\displaystyle x^{5}+ax+b=0}

satisfies Bring's curve since

{\\\\displaystyle \\\\sum _{i=1}^{5}x_{i}^{k}=0}

for

{\\\\displaystyle k=1,2,3.}