Algebraic cycles on Gushel-Mukai varieties
Algebraic Geometry
2026-05-27 v4
Abstract
We study algebraic cycles on complex Gushel-Mukai (GM) varieties. We prove the generalised Hodge conjecture, the (motivated) Mumford-Tate conjecture, and the generalised Tate conjecture for all GM varieties. We compute all integral Chow groups of GM varieties, except for the only two infinite-dimensional cases (1-cycles on GM fourfolds and 2-cycles on GM sixfolds). We prove that if two GM varieties are generalised partners or generalised duals, their rational Chow motives in middle degree are isomorphic.
Keywords
Cite
@article{arxiv.2207.01118,
title = {Algebraic cycles on Gushel-Mukai varieties},
author = {Lie Fu and Ben Moonen},
journal= {arXiv preprint arXiv:2207.01118},
year = {2026}
}
Comments
23 pages, final version, in special volume in honour of C. Voisin