{{Short description|Object in algebraic geometry}} 240px|right|thumb|The surface with {{math|1=''w'' = 1}} (real points, bounded by a sphere with radius=6). [[File:3D model of Togliatti surface (w=1).stl|thumb|3D model of same surface as above ({{math|1=''w'' = 1}}) bounded by the cube {{math|[-10, 10]{{sup|3}}}}]]
In algebraic geometry, a '''Togliatti surface''' is a nodal surface of degree five with 31 nodes. The first examples were constructed by {{harvs|txt|authorlink=Eugenio Giuseppe Togliatti|first=Eugenio G.|last= Togliatti|year=1940}}. {{harvs|txt|last = Beauville | first = Arnaud | author-link = Arnaud Beauville|year=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== *{{citation | last = Beauville | first = Arnaud | author-link = Arnaud Beauville | contribution = Sur le nombre maximum de points doubles d'une surface dans <math>\mathbf{P}^3 (\mu(5)=31)</math> | language = French | location = Alphen aan den Rijn—Germantown, Md. | mr = 605342 | pages = 207–215 | publisher = Sijthoff & Noordhoff | title = Journées de Géometrie Algébrique d'Angers, Juillet 1979/Algebraic Geometry, Angers, 1979 | url = http://math1.unice.fr/~beauvill/pubs/mu%285%29.pdf | year = 1980}}. *{{citation | last = Togliatti | first = Eugenio G. | author-link = Eugenio Giuseppe Togliatti | contribution = Una notevole superficie di 5<sup>o</sup> ordine con soli punti doppi isolati | language = Italian | mr = 0004492 | pages = 127–132 | series = Vierteljschr. Naturforsch. Ges. Zürich | title = Beiblatt (Festschrift Rudolf Fueter) | url = http://www.ngzh.ch/archiv/1940_85/85_BB32/85BB32_25.pdf | volume = 85 | year = 1940}}.
==External links== *{{Cite web|url=http://enriques.mathematik.uni-mainz.de/docs/Etogliatti.shtml|title=Togliatti surfaces|first=Stephan |last=Endraß|year=2003}} *{{mathworld|title=Togliatti surface|urlname=TogliattiSurface}}
Category:Algebraic surfaces Category:Complex surfaces
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