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Concept
Federigo Enriques
Summary
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.
Enriques was born in Livorno, and brought up in Pisa, in a Sephardi Jewish family of Portuguese descent. His younger brother was zoologist Paolo Enriques who was also the father of Enzo Enriques Agnoletti and Anna Maria Enriques Agnoletti. He became a student of Guido Castelnuovo (who later became his brother-in-law after marrying his sister Elbina), and became an important member of the Italian school of algebraic geometry. He also worked on differential geometry. He collaborated with Castelnuovo, Corrado Segre and Francesco Severi. He had positions at the University of Bologna, and then the University of Rome La Sapienza. In 1931 he sworn allegiance to fascism, and in 1933 he became a member of the PNF. Despite this, he lost his position in 1938, when the Fascist government enacted the "leggi razziali" (racial laws), which in particular banned Jews from holding professorships in Universities.
The Enriques classification, of complex algebraic surfaces up to birational equivalence, was into five main classes, and was background to further work until Kunihiko Kodaira reconsidered the matter in the 1950s. The largest class, in some sense, was that of surfaces of general type: those for which the consideration of differential forms provides linear systems that are large enough to make all the geometry visible. The work of the Italian school had provided enough insight to recognise the other main birational classes. Rational surfaces and more generally ruled surfaces (these include quadrics and cubic surfaces in projective 3-space) have the simplest geometry. Quartic surfaces in 3-spaces are now classified (when non-singular) as cases of K3 surfaces; the classical approach was to look at the Kummer surfaces, which are singular at 16 points.
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