论文标题
Gushel-Mukai品种上的代数周期
Algebraic cycles on Gushel-Mukai varieties
论文作者
论文摘要
我们研究了复杂的Gushel-Mukai（GM）品种的代数循环。我们证明了所有GM品种的广义霍奇猜想，（动机的）Mumford-Tate猜想和广义泰特猜想。我们计算了GM品种的所有积分Chow群，除了仅有两个无限维情况（GM四倍的1个循环和GM六倍的2个循环）。我们证明，如果两个GM品种是广义的伙伴或广义双重的，则它们在中等程度上的理性CHOW动机是同构的。
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.
