Algebraic cycles on Gushel-Mukai varieties

2022/07/03 by Lie Fu, Ben Moonen, B.J. Moonen · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #math.AG

paper · pdf · doi:10.46298/epiga.2024.9815

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.

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• Motivic multiplicativity of complete intersections

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