10 apr 2019 -- 14:00
Aula di Consiglio, Dip. Matematica, Università "La Sapienza", Roma
Abstract.
The Lüroth problem asks whether every unirational variety is rational. Over C, it has a positive answer for curves and surfaces, but fails in higher dimensions. In this talk, I will consider the Lüroth problem for geometrically rational varieties over a non-algebraically closed field k. Adapting in this context the strategy implemented by Clemens and Griffiths over C, I will describe new examples of k-varieties that are geometrically rational, k-unirational, but not k-rational. This is joint work with Olivier Wittenberg.