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Programma anno 2019/2018
Seminario Matematico e Fisico di Milano
Arnaud Beauville
Université de Nice
Recent progress on rationality problems

Lunedì 14 Maggio 2018, ore 15:30
Sala di Rappresentanza, Università di Milano, Via C. Saldini 50, Milano
Abstract
We say that an algebraic variety is unirational if it can be parametrized by rational functions, rational if moreover the parametrization can be chosen to be one-to-one. A very classical problem, called nowadays the Luroth problem, asks whether a unirational variety is necessarily rational. This holds for curves (Luroth, 1875) and for surfaces (Castelnuovo, 1894); after various unsuccessful attempts, it was shown in 1971 that the answer is quite negative in dimension 3: there are many examples of unirational varieties which are not rational. Up to 3 years ago the known examples in dimension >3 were quite particular, but a new idea of Claire Voisin has significantly improved the situation. I will survey the colorful history of the problem, then explain Voisin's idea, and how it leads to a number of new results.
MATHEMATICS IN A COMPLEX WORLD - Slides - Photo - Video |  | RISM | Lezioni Leonardesche | RISM3 |