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

Evgeny Shinder, Sergey Galkin

Research output: Working paper

Abstract / Description of output

We find a relation between a cubic hypersurface Y and its Fano variety of lines F(Y ) in the Grothendieck ring. We use this relation to study the Hodge structure of F(Y). Finally we investigate rationality of smooth cubic hypersurfaces. In particular we prove that if L=[A^1] is not a zero-divisor in the Grothendieck ring, then a general cubic fourfold is irrational.
Original languageEnglish
PublisherArXiv
Publication statusPublished - 2014

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