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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 ). 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.
The emphasis on algebraic surfaces—algebraic varieties of dimension two—followed on from an essentially complete geometric theory of algebraic curves (dimension 1). The position in around 1870 was that the curve theory had incorporated with Brill–Noether theory the Riemann–Roch theorem in all its refinements (via the detailed geometry of the theta-divisor).
In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers , an algebraic surface has complex dimension two (as a complex manifold , when it is non-singular ) and so of dimension four as a smooth manifold .
An algebraic surface is an algebraic variety of dimension two. The Enriques-Kodaira classification gives an overview of the possibilities. Over the complex numbers, a non-singular algebraic surface is an example of a 4-manifold
Volume one. Algebraic exterior calculus and local differential properties], Istituto Nazionale di Alta Matematica (in Italian), Roma: Docet edizioni universitarie, p. 520, MR 0049646, Zbl 0045.19702. [8] Segre, Beniamino (1951b), Arithmetical Questions on Algebraic Varieties, London: The Athlone Press, pp. V+55, MR 0043498, Zbl 0042.15204. [9]
Giacomo Albanese (11 July 1890 – 8 June 1947 [1]) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in the University of São Paulo, Brazil, in 1936.
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
In 1906, he obtained a theorem of existence of algebraic curves drawn on certain types of surfaces, thus beginning the search for the classification of rational surfaces. [2] Mobilized during World War I, Severi enlisted in the artillery. In 1921, he obtained the chair of algebraic geometry at La Sapienza University in Rome.