Federigo Enriques (5 January 1871 –14 June 1946)－藍色情懷

今日數學家

費代裡戈·恩裡克斯
Federigo Enriques (5 January 1871 –14 June 1946)

以下是當年今日出生的數學家：

1871	Enriques
1838	*Jordan*
1871	Fano
1884	Denjoy
1909	Kleene

以下是當年今日殞落的數學家：

1970	Born
1987	Shtokalo

Federigo Enriques (5 January 1871 –14 June 1946) was an Italian classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry. mathematician, now known principally as the first to give a

He was born in Livorno, and brought up in Pisa, in a Jewish family of Portuguese descent. He became a student of Guido Castelnuovo, 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. He lost his position in 1938, when the Fascistgovernment enacted the "leggi razziali" (racial laws), which inparticular 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 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 systemsthat are large enough to make all the geometry visible. The work of theItalian school had provided enough insight to recognise the other mainbirational 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. Abelian surfaces elliptic surfaces, which are fiber bundles over a curve with elliptic curves as fiber, having a finite number of modifications (so there is a bundle that is locally trivial actually over a curve less some points). The question of classification is to show that any surface, lying in projective space of any dimension, is in the birational sense (after blowing up and blowing down give rise to Kummer surfaces as quotients. There remains the class of of some curves, that is) accounted for by the models already mentioned.

No more than other work in the Italian school would the proofs by Enriques now be counted as complete and rigorous.Not enough was known about some of the technical issues: the geometersworked by a mixture of inspired guesswork and close familiarity withexamples. Oscar Zariski started to work in the 1930s on a more refined theory of birational mappings, incorporating commutative algebra methods. He also began work on the question of the classification for characteristic p, where new phenomena arise. The schools of Kodaira and Igor Shafarevich had put Enriques' work on a sound footing by about 1960.

Works

Enriques F. Lezioni di geometria descrittiva. Bologna, 1920.
Enriques F. Lezioni di geometria proiettiva. Italian ed. 1898 and german ed. 1903.
Enriques F. Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche. Bologna, 1915-1934. Volume 1, Volume 2, Volume 3-4
Severi F. Lezioni de geometria algebrica : geometria sopra una curva, superficie di Riemann-integrali abeliani. Italian ed. 1908 and german ed. 1921
Castelnouvo G., Enriques F. Die algebraischen Flaechen// Encyklopädie der mathematischen Wissenschaften, III C 6
Enriques F. Le superficie algebriche. Bologna, 1949