Algebraic and Arithmetic Geometry Seminar

A rationality criterion for varieties and applications to Fano threefolds

by Ciro Ciliberto (Roma)

Aula Seminari (Department of Mathematics)

Aula Seminari

Department of Mathematics


In  1938 U. Morin, improving on earlier results by G. Fano (1918), stated a projective classification theorem for varieties of dimension $n\geq 3$ whose general surface sections are rational. Although Morin's result is correct, his proof is wrong. In the first part of this talk I will explain how to fix Morin's argument by using ideas from Mori's theory already exploited by F. Campana and H. Flenner to attack a quite similar problem. This part is joint work with C. Fontanari. In the second part of the talk I will make some application to rationality of Fano threefolds.