Quintic Surface

A quintic surface is an algebraic surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not explicitly derive equations for such surfaces. Beauville (1978) subsequently proved that 31 double points was the maximum possible, and quintic surfaces having 31 ordinary double points are therefore sometimes called Togliatti surfaces. van Straten (1993) subsequently constructed a three-dimensional family of solutions and in 1994, Barth derived the example known as the dervish.

Examples of quartic surfaces include the dervish, kiss surface, peninsula surface, swallowtail catastrophe surface, and Togliatti surface.

See also

Algebraic Surface, Dervish, Kiss Surface, Ordinary Double Point, Peninsula Surface

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Beauville, A. "Surfaces algébriques complexes." Astérisque 54, 1-172, 1978.Endraß, S. "Togliatti Surfaces.", B. "Algebraic Surfaces.", E. G. "Una notevole superficie del 5^o ordine con soli punti doppi isolati." Vierteljschr. Naturforsch. Ges. Zürich 85, 127-132, 1940.Togliatti, E. "Sulle superfici monoidi col massimo numero di punti doppi." Ann. Mat. Pura Appl. 30, 201-209, 1949.van Straten, D. "A Quintic Hypersurface in P^4 with 130 Nodes." Topology 32, 857-864, 1993.

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Quintic Surface

Cite this as:

Weisstein, Eric W. "Quintic Surface." From MathWorld--A Wolfram Web Resource.

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