Algebraic cycles on certain hyperkähler fourfolds with an order 3 non-symplectic automorphism

Abstract

Let \(X\) be a hyperkähler variety, and assume \(X\) has a non-symplectic automorphism \(\sigma\) of order \(>\frac{1}{2}\dim X\). Bloch's conjecture predicts that the quotient \(X/<\sigma>\) should have trivial Chow group of \(0\)--cycles. We verify this for Fano varieties of lines on certain special cubic fourfolds having an order \(3\) non-symplectic automorphism.