Lecture----数学院晨兴数学中心

Title:	The rationality problem in algebraic geometry I
Speaker:	Mingmin Shen ()
Time:	2015-6-30, 15:30-17:00
Place:	N817
Abstract:	One fundamental problem in algebraic geometry is to determine whether a variety is rational or not. Here being rational can be understood as being isomorphic to the projective space modulo lower dimensional subvarieties on both sides. In the lectures, I will explain how the problem gets more complicated as dimension increases. After reviewing the classical solution in low dimensional case, I will explain the work of Clemens—Griffiths on cubic threefold. Then a major part will be devoted to the recent results obtained by Voisin and Totaro via cycle-theoretical approach. I will also discuss the case of cubic fourfolds where the question is still open.
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