• Source: Togliatti surface

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). Arnaud Beauville (1980) proved that 31 is the maximum possible number of nodes for a surface of this degree, showing this example to be optimal.




See also


Barth surface
Endrass surface
Sarti surface
List of algebraic surfaces




References


Beauville, Arnaud (1980), "Sur le nombre maximum de points doubles d'une surface dans





P


3


(
μ
(
5
)
=
31
)


{\displaystyle \mathbf {P} ^{3}(\mu (5)=31)}

", Journées de Géometrie Algébrique d'Angers, Juillet 1979/Algebraic Geometry, Angers, 1979 (PDF) (in French), Alphen aan den Rijn—Germantown, Md.: Sijthoff & Noordhoff, pp. 207–215, MR 0605342.
Togliatti, Eugenio G. (1940), "Una notevole superficie di 5o ordine con soli punti doppi isolati", Beiblatt (Festschrift Rudolf Fueter) (PDF), Vierteljschr. Naturforsch. Ges. Zürich (in Italian), vol. 85, pp. 127–132, MR 0004492.




External links


Endraß, Stephan (2003). "Togliatti surfaces".
Weisstein, Eric W. "Togliatti surface". MathWorld.

Kata Kunci Pencarian:

• Togliatti surface
• Togliatti (disambiguation)
• List of complex and algebraic surfaces
• Palmiro Togliatti
• Eugenio Giuseppe Togliatti
• Barth surface
• Algebraic geometry
• Labs septic
• Domenico Montesano
• Endrass surface