An atomic criterion for irrationality without quantum computations

The birational invariants introduced by Katzarkov-Kontsevich-Pantev-Yu allows one to obtain irrationality results for varieties whose quantum cohomology is well-behaved.

We observe that under certain cohomological conditions, we can deduce irrationality of a very general member from the theory of atoms without actually computing them, using only monodromy equivariance of quantum multiplication and irreducibility of the monodromy representation.

Our criterion applies to the very general cubic and Gushel-Mukai fourfolds, whose irrationalities were already known, but also to the very general K{ü}chle fourfold of type (c5), which is a Fano manifold of index one.