Seckin Adali​ (UiO): The Artin-Mumford counterexample to the Lüroth problem

Abstract: In this talk, we will review the example of Artin and Mumford of a complex unirational 3-fold which is not rational. We will look at its construction to see why it is unirational. We will make use of the Brauer groups to see that there is non-trivial torsion in its 3rd singular cohomology group, which in turn implies that it is not stably-rational. Finally, we will briefly discuss the role of Brauer groups in other non-rationality results.