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

Source abstract

We prove the Beauville--Voisin conjecture for a very general Debarre--Voisin hyperkähler fourfold \(Y\subset\Gr(6,10)\) associated with a trivector $σ$ 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.