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Séminaire Géométries ICJ

On the Lüroth problem for real varieties

by Olivier Wittenberg

vendredi 27 avril 2018 de au (Europe/Paris)
at 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.