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

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.