The Geometers
According to Guerraggio & Nastasi (page 9, 2005) Luigi Cremona is "considered the founder of the Italian school of algebraic geometry". Later they explain that in Turin the collaboration of D'Ovidio and Corrado Segre "would bring, either by their own efforts or those of their students, Italian algebraic geometry to full maturity". A one-time student of Segre, H.F. Baker wrote (1926, page 269), "may probably be said to be the father of that wonderful Italian school which has achieved so much in the birational theory of algebraical loci." On this topic, Brigaglia & Ciliberto (2004) say "Segre had headed and maintained the school of geometry that Luigi Cremona had established in 1860." Reference to the Mathematics Genealogy Project shows that, in terms of Italian doctorates, the real productivity of the school began with Guido Castelnuovo and Federigo Enriques. In the USA Oscar Zariski inspired many Ph.D.s.
The roll of honour of the school includes the following other Italians: Giacomo Albanese, Bertini, Campedelli, Oscar Chisini, Michele De Franchis, Pasquale del Pezzo, Beniamino Segre, Francesco Severi, Guido Zappa (with contributions also from Gino Fano, Rosati, Torelli, Giuseppe Veronese).
Elsewhere it involved H. F. Baker and Patrick du Val (UK), Arthur Byron Coble (USA), Georges Humbert and Charles Émile Picard (France), Lucien Godeaux (Belgium), Hermann Schubert and Max Noether, and later Erich Kähler (Germany), H. G. Zeuthen (Denmark).
These figures were all involved in algebraic geometry, rather than the pursuit of projective geometry as synthetic geometry, which during the period under discussion was a huge (in volume terms) but secondary subject (when judged by its importance as research).
Read more about this topic: Italian School Of Algebraic Geometry