
Modul: MAT770 Oberseminar: Algebraische Geometrie
The stable Lüroth problem
Prof. Dr. Arnaud Beauville's talk Date: 02.03.15 Time: 13.15  14.45 Room: Y27H25 The classical Lüroth problem asks whether a variety which is unirational (= dominated by a projective space) is necessarily rational (= birational to a projective space). We know since 1971 that the answer is quite negative : at least in dimension 3, there are by now many examples of unirational varieties which are not rational. Hence the idea of looking for an intermediate property : a variety X is stably rational if X x P^n is rational for n >> 0. Till last year the known examples of unirational, non stably rational varieties were rare and very particular, but a new idea of Claire Voisin has significantly improved the situation. I'll explain this idea, and how it leads to new examples, particularly in dimension >3.

