Quintic Surface

A quintic surface is an Algebraic Surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31Ordinary Double Points exist, although he did not explicitly derive equations for suchsurfaces. Beauville (1978) subsequently proved that 31 double points was the maximum possible, and quintic surfaces having 31Ordinary Double Points are therefore sometimes called Togliatti Surfaces. van Straten (1993) subsequently constructed a 3-D family of solutions and in 1994, Barth derived the example knownas the Dervish.

References

Beauville, A. ``Surfaces algébriques complexes.'' Astérisque 54, 1-172, 1978.

Endraß, S. ``Togliatti Surfaces.''http://www.mathematik.uni-mainz.de/AlgebraischeGeometrie/docs/Etogliatti.shtml.

Hunt, B. ``Algebraic Surfaces.'' http://www.mathematik.uni-kl.de/~wwwagag/Galerie.html.

Togliatti, E. G. ``Una notevole superficie de ordine con soli punti doppi isolati.'' Vierteljschr. Naturforsch. Ges. Zürich 85, 127-132, 1940.

Togliatti, E. ``Sulle superficie monoidi col massimo numero di punti doppi.'' Ann. Mat. Pura Appl. 30, 201-209, 1949.

van Straten, D. ``A Quintic Hypersurface in with Nodes.'' Topology 32, 857-864, 1993.

• Poincaré Manifold
• Poincaré Metric
• Poincaré Separation Theorem
• Poincaré's Holomorphic Lemma
• Poincaré's Lemma
• Poinsot Solid
• Poinsot's Spirals
• Point
• Point at Infinity
• Point Estimator
• Point Groups
• Point-Line Distance--2-D
• Point-Line Distance--3-D
• Point Picking
• Point-Plane Distance
• Point-Point Distance--1-D
• Point-Point Distance--2-D
• Point-Point Distance--3-D
• Point Probability
• Point-Quadratic Distance
• Point-Set Topology
• Points Problem
• Pointwise Dimension
• Poisson Bracket
• Poisson-Charlier Function