The surface of Togliatti
The Togliatti surface is an algebraic surface of the fifth degree. It has the maximum possible number of features among the fifth degree curves.
History
Described by the Italian mathematician Eugenio Tolyatti in 1940.
Tolyatti built an example for 31 features ( double points ). In 1979, Arnaud Beauville proved that this is the maximum possible number of features.
In 1993, van Straten found three-dimensional solutions to the equation, and Barth in 1994 built a concrete example called the “ dervish ”.
Literature
- Eugenio Togliatti. Una notevole superficie de 5 o ordine con soli punti doppi isolati // Vierteljschr. Naturforsch. Ges. Zürich 85. - Zurich , 1940.- T. 85 . - S. 127–132 .
Links
- Endraß, Stephan Togliatti surfaces (2003). Date of treatment June 8, 2012. Archived September 24, 2012.
- Weisstein, Eric W. Togliatti surface ( Wolfram ) at Wolfram MathWorld .
- Eric W. Weisstein. Dervish . Concise Encyclopedia of Mathematics . Date of treatment June 22, 2014.