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

ABSTRACT

Let X be a hyperkähler variety, and assume X has a non-symplectic automorphism σ of order $k>\frac{1}{2}dimX$. Bloch’s conjecture predicts that the quotient X∕<σ> 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.

KEYWORDS:

• Algebraic cycles
• Beauville’s “splitting property” conjecture
• Bloch–Beilinson filtration
• Bloch’s conjecture
• Chow group
• Fano varieties of lines on cubic fourfolds
• finite-dimensional motive
• hyperkähler varieties
• motive
• non-symplectic automorphism

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 14C15
• 14C25
• 14C30

Acknowledgement

Thanks to all participants of the Strasbourg 2014/2015 “groupe de travail” based on the monograph [47] for a very stimulating atmosphere. Many thanks to Mrs. Yasuyo Ishitani, Director of the Special Program “O-Uchi De O-Shigoto”, for an excellent working environment.