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Working paper

The Fano variety of lines and rationality problem for a cubic hypersurface

arxiv.org. math. Cornell University, 2014. No. 1405.5154.
Galkin S., Shinder E.
We find a relation between a cubic hypersurface Y and its Fano variety of lines F(Y) 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.