Search results
Results from the WOW.Com Content Network
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).
Every irreducible complex algebraic curve is birational to a unique smooth projective curve, so the theory for curves is trivial. The case of surfaces was first investigated by the geometers of the Italian school around 1900; the contraction theorem of Guido Castelnuovo essentially describes the process of constructing a minimal model of any smooth projective surface.
The theory of algebraic surfaces is much more complicated than that of algebraic curves (including the compact Riemann surfaces, which are genuine surfaces of (real) dimension two). Many results were obtained, but, in the Italian school of algebraic geometry , and are up to 100 years old.
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.
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
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
Abramo Giulio Umberto Federigo Enriques (5 January 1871 – 14 June 1946) was an Italian mathematician, now known principally as the first to give a classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry.
Francesco Severi (13 April 1879 – 8 December 1961) was an Italian mathematician. He was the chair of the committee on Fields Medal in 1936, at the first delivery. Severi was born in Arezzo, Italy. He is famous for his contributions to algebraic geometry and the theory of functions of several complex variables.