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.
"A remark on the Chow ring of some hyperkähler fourfolds." Bull. Belg. Math. Soc. Simon Stevin 24 (3) 447 - 455, september 2017. https://doi.org/10.36045/bbms/1506477693