Abstract
We propose an explicit conjectural lift of the Neron–Severi Lie algebra of a hyperkähler variety X of K3^{[2]}-type to the Chow ring of correspondences mathrm{CH}^*(X times X) in terms of a canonical lift of the Beauville–Bogomolov class obtained by Markman. We give evidence for this conjecture in the case of the Hilbert scheme of two points of a K3 surface and in the case of the Fano variety of lines of a very general cubic fourfold. Moreover, we show that the Fourier decomposition of the Chow ring of X of Shen and Vial agrees with the eigenspace decomposition of a canonical lift of the cohomological grading operator.
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