The diagonal of (3,3) fivefolds
arXiv:2303.00562
Abstract
We show that a very general (3,3) complete intersection in over an algebraically closed uncountable field of characteristic different from 2 admits no decomposition of the diagonal, in particular it is not retract rational. This strengthens Nicaise--Ottem's result, where stable irrationality in characteristic 0 was shown. The main tool is a Chow-theoretic obstruction which was found by Pavic--Schreieder, where quartic fivefolds are studied.
20 pages, final version, to appear in Annales de l'Institut Fourier