Seminario / Beauville
Lunedì 14 maggio 2018, alle ore 15:30 precise
presso la Sala di Rappresentanza del Dipartimento di Matematica,
Università di Milano in Via Saldini 50
Prof. ARNAUD BEAUVILLE
Université de Nice
"Recent progress on rationality problems"
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.
Tutti gli interessati sono invitati a partecipare.
Il direttore del Seminario
Per ulteriori informazioni sulle attività del seminario: http://www.mate.polimi.it/smf