Togliatti Surface
Togliatti (1940, 1949) showed that Quintic Surfaces having 31 Ordinary DoublePoints exist, although he did not explicitly derive equations for such surfaces. Beauville (1978)subsequently proved that 31 double points are the maximum possible, and quintic surfaces having 31 Ordinary DoublePoints are therefore sometimes called Togliatti surfaces. van Straten (1993) subsequentlyconstructed a 3-D family of solutions and in 1994, Barth derived the example known as the Dervish.
See also Dervish, Ordinary Double Point, Quintic Surface
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.
- Linear Equation System
- Linear Extension
- Linear Fractional Transformation
- Linear Group
- Linear Group Theorem
- Linearly Dependent Curves
- Linearly Dependent Functions
- Linearly Dependent Vectors
- Linearly Independent
- Linear Operator
- Linear Ordinary Differential Equation
- Linear Programming
- Linear Recurrence Sequence
- Linear Regression
- Linear Space
- Linear Stability
- Linear Transformation
- Line at Infinity
- Line Bisector
- Line Element
- Line Graph
- Line Integral
- Line of Curvature
- Line Segment
- Line Space