Speaker: Sergey Galkin

Title: Cubics: lines, squares, and irrationality

Date: Mar 14, 2014, 12:00 - 12:50

Place: Playa del Carmen

Abstract:

I will describe our joint work with Evgeny Shinder.
We prove that generic cubic fourfold is irrational
under the assumption that
the class of an affine line is not a zero divisor in the Grothendieck ring of complex varieties.
Main new geometric ingredient of the proof is a beautiful formula,
that relates classes of a cubic hypersurface itself,
its symmetric square, variety of lines and the singular locus.
The formula is unconditional and holds over any reduced cubic hypersurface over arbitrary field.