Evento
Descrizione:
Abstract: The Lüroth problem asks whether every unirational variety is rational. Over the complex numbers, it has a positive answer for curves and surfaces, but fails in higher dimensions. In this talk, I will consider the Lüroth problem 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 k-unirational, rational over the algebraic closure of k, but not k-rational. This is joint work with Olivier Wittenberg.