On the motive of some hyperKaehler varieties

Abstract

We show that the motive of the Hilbert scheme of length-$n$ subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, Beauville, and Deninger and Murre.

9 pages. To appear in Crelle's journal

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• Algebraic cycles and intersections of three quadrics
• Algebraic cycles and intersections of 2 quadrics
• On the Chow ring of Fano varieties on the Fatighenti-Mongardi list
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