Togliatti surface

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The surface with
{\displaystyle w=1}
(real points, bounded by a sphere with radius=6). Togliatti surface.png
The surface with (real points, bounded by a sphere with radius=6).
3D model of same surface as above (
{\displaystyle w=1}
) bounded by the cube
{\displaystyle [-10,10]^{3}} 3D model of Togliatti surface (w=1).stl
3D model of same surface as above () bounded by the cube

In algebraic geometry, a Togliatti surface is a nodal surface of degree five with 31 nodes. The first examples were constructed by Eugenio G.Togliatti  ( 1940 ). ArnaudBeauville  ( 1980 ) proved that 31 is the maximum possible number of nodes for a surface of this degree, showing this example to be optimal.


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