论文标题
有效的零循环和Bloch-Beilinson过滤
Effective zero-cycles and the Bloch-Beilinson filtration
论文作者
论文摘要
Voisin的一个猜想指出，在平滑的投射复合体上的两个点在第2级中产生了圆形形式的代数，而当它们的差异在Bloch-Bebeilinson Filtration的第三步中，彼此之间是彼此之间相互等同的。在本说明中，我们制定了一个概括，该概括使有效的零循环具有合理的等效性，而牺牲了在Bloch-Beilinson过滤中更深入的看法。在上半年，我们提供了支持该猜想的证据，如果是Abelian品种和投射Hyper-Kähler歧管。值得注意的是，我们给出了有效的零循环在K3表面上可半固定滑轮的模量空间上合理等效的明确标准，从而概括了Marian-Zhao。在下半场，为了解释我们的主要猜想，我们制定了第二个猜想，以预测平滑射击品种的对角线何时属于低度以低度产生的对应关系的子代数。
A conjecture of Voisin states that two points on a smooth projective complex variety whose algebra of holomorphic forms is generated in degree 2 are rationally equivalent to each other if and only if their difference lies in the third step of the Bloch-Beilinson filtration. In this note, we formulate a generalization that allows for rational equivalence of effective zero-cycles of higher degree, at the expense of looking deeper in the Bloch-Beilinson filtration. In the first half, we provide evidence in support of this conjecture in the case of abelian varieties and projective hyper-Kähler manifolds. Notably, we give explicit criteria for rational equivalence of effective zero-cycles on moduli spaces of semistable sheaves on K3 surfaces, generalizing that of Marian-Zhao. In the second half, in an effort to explain our main conjecture, we formulate a second conjecture predicting when the diagonal of a smooth projective variety belongs to a subalgebra of the ring of correspondences generated in low degree.
