Ambient Chow Rings of Debarre--Voisin Fourfolds and the Beauville--Voisin Conjecture

We prove the Beauville–Voisin conjecture for a very general Debarre–Voisin hyperkähler fourfold $Y\subset \text{Gr}(6,10)$ associated with a trivector $\sigma$ on a ten-dimensional complex vector space $V_{10}$. Namely, the cycle class map is injective on the subalgebra of the Chow ring generated by divisor classes and the Chern classes of the tangent bundle.