Paper
The Fano variety of lines and rationality problem for a cubic hypersurface
Authors
Sergey Galkin, Evgeny Shinder
Abstract
We find a relation between a cubic hypersurface and its Fano variety of lines in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then Fano variety of lines on a smooth rational cubic fourfold is birational to a Hilbert scheme of two points on a K3 surface; in particular, general cubic fourfold is irrational.