Which employer did Federigo Enriques work for in Apr 1892?
Federigo Enriques 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 . Biography . 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 . 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 . Abelian surfaces give rise to Kummer surfaces as quotients . There remains the class of 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 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 geometers worked by a mixture of inspired guesswork and close familiarity with examples . 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 Kunihiko 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 . & Chisini , O . Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche . Bologna , 1915-1934 . Volume 1 , Volume 2 , Vol . 3 , 1924 ; Vol . 4 , 1934 . - Severi F . Lezioni di geometria algebrica : geometria sopra una curva , superficie di Riemann-integrali abeliani . Italian ed . 1908 . - Enriques F . Problems of Science ( trans . Problemi di Scienza ) . Chicago , 1914 . - Enriques F . Zur Geschichte der Logik . Leipzig , 1927 . - Castelnouvo G. , Enriques F . Die algebraischen Flaechen// Encyklopädie der mathematischen Wissenschaften , III C 6 - Enriques F . Le superficie algebriche . Bologna , 1949 . Articles . On Scientia . - Eredità ed evoluzione - I numeri e linfinito - Il pragmatismo - Il principio di ragion sufficiente nel pensiero greco - Il problema della realtà - Il significato della critica dei principii nello sviluppo delle matematiche - Importanza della storia del pensiero scientifico nella cultura nazionale - Linfini dans la pensee des grecs - Linfinito nella storia del pensiero - Loeuvre mathematique de Klein - La connaissance historique et la connaissance scientifique dans la critique de Enrico De Michelis - La filosofia positiva e la classificazione delle scienze - I motivi della filosofia di Eugenio Rignano External links . - Reviews of the works of Federigo Enriques , MacTutor History - PRISTEM page ( Italian language ) - Official home page of center for Enriques studies ( Italian language )