2000 character limit reached
The Fano variety of lines and rationality problem for a cubic hypersurface (1405.5154v2)
Published 20 May 2014 in math.AG
Abstract: 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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.