论文标题
$ k3^{[2]} $的Hyperkähler品种的食物环 - 通过lefschetz Action键入
The Chow ring of hyperkähler varieties of $K3^{[2]}$-type via Lefschetz actions
论文作者
论文摘要
我们提出了neron-severi lie代数的明确猜想提升，$ x $的$ x $ of $ k3^{[2]} $ - 键入$ {\ rm ch}^\ rm ch}^\ ast（x \ ast x \ ast x \ times x）$，以beauville-bogomolov carks vertaind class vernical class crom by rank by rark cover。如果希尔伯特方案为$ k3 $ $ k3 $的表面，并且在非常普遍的立方四倍的范诺（Fano）各种线上，我们给出了这一猜想的证据。此外，我们表明，$ x $ of Shen和Vial的Chow环的傅立叶分解与分级运算符的规范升降机的特征分解相一致。
We propose an explicit conjectural lift of the Neron-Severi Lie algebra of a hyperkähler variety $X$ of $K3^{[2]}$-type to the Chow ring of correspondences ${\rm CH}^\ast(X \times X)$ in terms of a canonical lift of the Beauville-Bogomolov class obtained by Markman. We give evidence for this conjecture in the case of the Hilbert scheme of two points of a $K3$ surface and in the case of the Fano variety of lines of a very general cubic fourfold. Moreover, we show that the Fourier decomposition of the Chow ring of $X$ of Shen and Vial agrees with the eigenspace decomposition of a canonical lift of the grading operator.
