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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.