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Motivic decompositions for the Hilbert scheme of points of a K3 surface

Andrei Neguţ ORCID logo, Georg Oberdieck and Qizheng Yin

Abstract

We construct an explicit, multiplicative Chow–Künneth decomposition for the Hilbert scheme of points of a K3 surface. We further refine this decomposition with respect to the action of the Looijenga–Lunts–Verbitsky Lie algebra.

Funding statement: Andrei Neguţ gratefully acknowledges the NSF grants DMS-1760264 and DMS-1845034, as well as support from the Alfred P. Sloan Foundation. Qizheng Yin was supported by the NSFC grants 11701014, 11831013, and 11890661.

Acknowledgements

We would like to thank Lie Fu, Alina Marian, Davesh Maulik, Junliang Shen, Catharina Stroppel, and Zhiyu Tian for useful discussions.

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Received: 2020-01-07
Revised: 2020-04-28
Published Online: 2021-04-19
Published in Print: 2021-09-01

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