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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).
His life was devoted to the study of geometry and reforming advanced mathematical teaching in Italy. He worked on algebraic curves and algebraic surfaces, particularly through his paper Introduzione ad una teoria geometrica delle curve piane ("Introduction to a geometrical theory of the plane curves"), and was a founder of the Italian school of ...
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.
Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces; Zariski surfaces, surfaces in finite characteristic that admit a purely inseparable dominant rational map from the projective plane
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
Among his main contributions to algebraic geometry are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His work was in the style of the old Italian School , although he also appreciated the greater rigour of modern algebraic geometry.
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 .
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.