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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).
To the east, Salento is 70 km (43 mi) from the Albanian coast, [6] at the narrowest point of the Strait of Otranto. It is Capo d'Otranto (also called Punta Palascìa), located at 40° 7' north latitude and 18° 31' east longitude. To the north of Salento lies the long and narrow inlet of the Adriatic Sea. Map of the climate of Italy
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.
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.
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.
Italy in a map dated 1853. In a narrow sense, the continental part, delimited to the north by the Alpine watershed, to about 40% of the Italian region and is located in the north of an imaginary line that goes from the mouth of the Magra river to that of the Rubicone river.