Speaker: Sergey Galkin

Title: Grothendieck's constructor and irrationality of cubic fourfolds

Date: Mar 29, 2014, 11:30

Place: University of Geneva

This is second part of the story. I will introduce Grothendieck ring of varieties (ring of generalized Euler characteristic or so-called "motivic measures") and show how it could be used for solving rationality problems, using theorem of Larsen and Lunts. I will demonstrate a beautiful identity in this ring, that relates symmetric square of cubic hypersurface with its Fano variety of lines. We will use this identity to show, that if class of an affine line is not a zero divisor in the Grothendieck ring of complex varieties, then variety of lines on a rational cubic fourfold is birational to symmetric square of a K3 surface, in particular, generic cubic fourfold is irrational. This is a joint work with Evgeny Shinder.