Algebraic cycles on certain hyperkaehler fourfolds with an order $3$ non-symplectic automorphism II

Abstract

Let $X$ be a hyperkähler variety, and assume that $X$ admits a non-symplectic automorphism $\sigma$ of order $k>\frac{1}{2}\dim X$. 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 cubic fourfolds having an order $3$ non-symplectic automorphism.

To appear in Comm. Algebra, 28 pages. This is a sequel to arxiv:1712.05981, which explains the text overlap

References in corpus (3)

• The generalized Franchetta conjecture for some hyper-Kähler varieties
• On the rationality and the finite dimensionality of a cubic fourfold
• Bloch's conjecture for the surface of Craighero and Gattazzo