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- Federigo_Enriques abstract "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.He was born in Livorno, and brought up in Pisa, in a Sephardi 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 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.".
- Federigo_Enriques almaMater Scuola_Normale_Superiore_di_Pisa.
- Federigo_Enriques birthDate "1871-01-05".
- Federigo_Enriques birthPlace Livorno.
- Federigo_Enriques deathDate "1946-06-14".
- Federigo_Enriques deathPlace Rome.
- Federigo_Enriques doctoralAdvisor Enrico_Betti.
- Federigo_Enriques doctoralAdvisor Guido_Castelnuovo.
- Federigo_Enriques doctoralStudent Paul_Libois.
- Federigo_Enriques doctoralStudent Pol_Burniat.
- Federigo_Enriques field Mathematics.
- Federigo_Enriques knownFor Enriques_surface.
- Federigo_Enriques nationality Italy.
- Federigo_Enriques thumbnail Federigo_Enriques.jpg?width=300.
- Federigo_Enriques wikiPageExternalLink enriques.le-superficie-algebriche.1949.300dpi.djvu.
- Federigo_Enriques wikiPageExternalLink D215715.html.
- Federigo_Enriques wikiPageExternalLink enriques.htm.
- Federigo_Enriques wikiPageExternalLink ACV3026.0001.001.
- Federigo_Enriques wikiPageExternalLink ACV3262.0001.001.
- Federigo_Enriques wikiPageExternalLink ACV4849.0001.001.
- Federigo_Enriques wikiPageExternalLink www.centrostudienriques.it.
- Federigo_Enriques wikiPageExternalLink lexgeoalgageo00severich.
- Federigo_Enriques wikiPageExternalLink lezioniteoriageo01enririch.
- Federigo_Enriques wikiPageExternalLink lezioniteoriageo02enririch.
- Federigo_Enriques wikiPageExternalLink vorluberalgebrais00severich.
- Federigo_Enriques wikiPageID "1732661".
- Federigo_Enriques wikiPageLength "8196".
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- Federigo_Enriques wikiPageRevisionID "708208281".
- Federigo_Enriques wikiPageWikiLink Abelian_surface.
- Federigo_Enriques wikiPageWikiLink Algebraic_geometry.
- Federigo_Enriques wikiPageWikiLink Algebraic_surface.
- Federigo_Enriques wikiPageWikiLink Birational_geometry.
- Federigo_Enriques wikiPageWikiLink Blowing_down.
- Federigo_Enriques wikiPageWikiLink Blowing_up.
- Federigo_Enriques wikiPageWikiLink Category:1871_births.
- Federigo_Enriques wikiPageWikiLink Category:1946_deaths.
- Federigo_Enriques wikiPageWikiLink Category:20th-century_Italian_mathematicians.
- Federigo_Enriques wikiPageWikiLink Category:20th-century_Italian_philosophers.
- Federigo_Enriques wikiPageWikiLink Category:Algebraic_geometers.
- Federigo_Enriques wikiPageWikiLink Category:Historians_of_mathematics.
- Federigo_Enriques wikiPageWikiLink Category:Italian_Jews.
- Federigo_Enriques wikiPageWikiLink Category:Italian_people_of_Portuguese_descent.
- Federigo_Enriques wikiPageWikiLink Category:People_from_Livorno.
- Federigo_Enriques wikiPageWikiLink Category:Sapienza_University_of_Rome_faculty.
- Federigo_Enriques wikiPageWikiLink Category:Spanish_and_Portuguese_Jews.
- Federigo_Enriques wikiPageWikiLink Characteristic_(algebra).
- Federigo_Enriques wikiPageWikiLink Commutative_algebra.
- Federigo_Enriques wikiPageWikiLink Corrado_Segre.
- Federigo_Enriques wikiPageWikiLink Cubic_surface.
- Federigo_Enriques wikiPageWikiLink Differential_form.
- Federigo_Enriques wikiPageWikiLink Differential_geometry.
- Federigo_Enriques wikiPageWikiLink Elliptic_curve.
- Federigo_Enriques wikiPageWikiLink Elliptic_surface.
- Federigo_Enriques wikiPageWikiLink Enrico_Betti.
- Federigo_Enriques wikiPageWikiLink Enriques_surface.
- Federigo_Enriques wikiPageWikiLink Enriques–Kodaira_classification.
- Federigo_Enriques wikiPageWikiLink Fascism.
- Federigo_Enriques wikiPageWikiLink Fiber_bundle.
- Federigo_Enriques wikiPageWikiLink Francesco_Severi.
- Federigo_Enriques wikiPageWikiLink Guido_Castelnuovo.
- Federigo_Enriques wikiPageWikiLink Igor_Shafarevich.
- Federigo_Enriques wikiPageWikiLink Italian_school_of_algebraic_geometry.
- Federigo_Enriques wikiPageWikiLink Italy.
- Federigo_Enriques wikiPageWikiLink K3_surface.
- Federigo_Enriques wikiPageWikiLink Kummer_surface.
- Federigo_Enriques wikiPageWikiLink Kunihiko_Kodaira.
- Federigo_Enriques wikiPageWikiLink Linear_system.
- Federigo_Enriques wikiPageWikiLink Livorno.
- Federigo_Enriques wikiPageWikiLink Mathematics.
- Federigo_Enriques wikiPageWikiLink Oscar_Zariski.
- Federigo_Enriques wikiPageWikiLink Paul_Libois.
- Federigo_Enriques wikiPageWikiLink Pisa.
- Federigo_Enriques wikiPageWikiLink Pol_Burniat.
- Federigo_Enriques wikiPageWikiLink Portugal.
- Federigo_Enriques wikiPageWikiLink Projective_space.
- Federigo_Enriques wikiPageWikiLink Quadric.
- Federigo_Enriques wikiPageWikiLink Quartic_surface.
- Federigo_Enriques wikiPageWikiLink Rational_surface.
- Federigo_Enriques wikiPageWikiLink Rigour.
- Federigo_Enriques wikiPageWikiLink Rome.
- Federigo_Enriques wikiPageWikiLink Ruled_surface.
- Federigo_Enriques wikiPageWikiLink Sapienza_University_of_Rome.
- Federigo_Enriques wikiPageWikiLink Scuola_Normale_Superiore_di_Pisa.
- Federigo_Enriques wikiPageWikiLink Sephardi_Jews.
- Federigo_Enriques wikiPageWikiLink Singular_point_of_an_algebraic_variety.
- Federigo_Enriques wikiPageWikiLink Surface_of_general_type.
- Federigo_Enriques wikiPageWikiLink University_of_Bologna.
- Federigo_Enriques wikiPageWikiLinkText "Enriques".
- Federigo_Enriques wikiPageWikiLinkText "Enriques, Federigo".
- Federigo_Enriques wikiPageWikiLinkText "Federigo Enriques".
- Federigo_Enriques almaMater Scuola_Normale_Superiore_di_Pisa.
- Federigo_Enriques birthDate "1871-01-05".
- Federigo_Enriques birthPlace Livorno.
- Federigo_Enriques deathDate "1946-06-14".
- Federigo_Enriques deathPlace Rome.
- Federigo_Enriques doctoralAdvisor Enrico_Betti.
- Federigo_Enriques doctoralAdvisor Guido_Castelnuovo.
- Federigo_Enriques doctoralStudents Paul_Libois.
- Federigo_Enriques doctoralStudents Pol_Burniat.