Algebraic cycles on certain hyperkaehler 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.

arXiv comment15 pages, to appear in North Western European J. of Math., comments welcome. arXiv admin note: text overlap with arXiv:1708.06092, arXiv:1704.01083