Rocky Mountain Journal of Mathematics

On Chow groups of some hyperkahler fourfolds with a non-symplectic involution, II

Robert Laterveer

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Abstract

This note is about hyperkahler fourfolds $X$ admitting a non-symplectic involution $\iota $. The Bloch-Beilinson conjectures predict the way $\iota $ should act on certain pieces of the Chow groups of $X$. The main result of this note is a verification of this prediction for Fano varieties of lines on certain cubic fourfolds. This has some interesting consequences for the Chow ring of the quotient $X/\iota $.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 6 (2018), 1925-1950.

Dates
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1543028446

Digital Object Identifier
doi:10.1216/RMJ-2018-48-6-1925

Mathematical Reviews number (MathSciNet)
MR3879310

Zentralblatt MATH identifier
06987233

Subjects
Primary: 14C15: (Equivariant) Chow groups and rings; motives 14C25: Algebraic cycles 14C30: Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture

Keywords
Algebraic cycles Chow groups motives Bloch's conjecture Bloch-Beilinson filtration hyperkahler varieties non-symplectic involution multiplicative Chow-Künneth decomposition splitting property Calabi-Yau varieties

Citation

Laterveer, Robert. On Chow groups of some hyperkahler fourfolds with a non-symplectic involution, II. Rocky Mountain J. Math. 48 (2018), no. 6, 1925--1950. doi:10.1216/RMJ-2018-48-6-1925. https://projecteuclid.org/euclid.rmjm/1543028446


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