Séminaire Géométries ICJ

On the Lüroth problem for real varieties

by Olivier Wittenberg

Fokko du Cloux (ICJ)

Fokko du Cloux


1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
(Joint work with Olivier Benoist.) The Lüroth problem asks whether unirational varieties are rational. It has a positive answer for complex curves and surfaces; negative answers for complex threefolds have been understood since the 70's. I will discuss 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 a nontrivial unramified cohomology group over the reals.