Togliatti surface

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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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References

• Beauville, Arnaud (1980), "Sur le nombre maximum de points doubles d'une surface dans ${\displaystyle \mathbf {P} ^{3}(\mu (5)=31)}$", 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 .