Bulletin of the Belgian Mathematical Society - Simon Stevin

A remark on the Chow ring of some hyperkähler fourfolds

Robert Laterveer

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Abstract

Let $X$ be a hyperkähler variety. Voisin has conjectured that the classes of Lagrangian constant cycle subvarieties in the Chow ring of $X$ should lie in a subring injecting into cohomology. We study this conjecture for the Fano variety of lines on a very general cubic fourfold.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 3 (2017), 447-455.

Dates
First available in Project Euclid: 27 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1506477693

Digital Object Identifier
doi:10.36045/bbms/1506477693

Mathematical Reviews number (MathSciNet)
MR3706813

Zentralblatt MATH identifier
06803442

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--Beilinson filtration hyperkähler varieties Fano variety of lines on cubic fourfold Beauville's splitting principle multiplicative Chow--Künneth decomposition spread of algebraic cycles

Citation

Laterveer, Robert. A remark on the Chow ring of some hyperkähler fourfolds. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 3, 447--455. doi:10.36045/bbms/1506477693. https://projecteuclid.org/euclid.bbms/1506477693


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