On the Lüroth problem for real varieties
Apparaît également dans la collection : Birational geometry and Hodge theory / Géométrie birationnelle et théorie de Hodge
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 for real algebraic varieties that are geometrically rational, and explain a counterexample not accounted for by the topology of the real locus or by unramified cohomology. This is joint work with Olivier Wittenberg.