Speaker: Sergey Galkin

Title: Rational cubic fourfolds, their lines, and associated K3 surfaces

Date: May 1, 2014, 9:30 - 11:00

Place: Istanbul Centre for Mathematical Sciences

This is a joint work with Evgeny Shinder. Assume that an affine line is not a zero divisor in the Grothendieck ring of complex varieties. We show that under this assumption the variety of lines on a rational cubic fourfold is birational to a Hilbert scheme of two points on a K3 surface. In particular, this implies conjecture of Hassett on Hodge structures, which in turn implies conjecture of V.A.Iskovskikh: rational cubic fourfolds have rank of algebraic cycles at least two, in particular, generic cubic fourfold is irrational.