Speaker: Sergey Galkin

Title: Cubics: lines, squares, and irrationality

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

Place: Playa del Carmen

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.

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