论文标题
在Lefschetz的标准猜想上
On the Lefschetz standard conjecture for Lagrangian covered hyper-Kähler varieties
论文作者
论文摘要
我们调查了Lefschetz标准猜想的学位$ 2 $ Hyper-Kähler歧管的共同体，承认Lagranganian Subvarieties的掩护。在拉格朗日纤维化的情况下，我们表明lefschetz标准猜想是由表征与拉格朗日纤维相关的分层类别的Syz猜想所暗示的。在尺寸$ 4 $中，我们考虑了Lagrangian覆盖的四倍$ x $的更一般情况，并证明Lefschetz标准猜想为$ 2 $，假设$ρ（x）= 1 $和$ x $是Moduli的一般。最后，我们讨论了Lefschetz循环与研究点和Bloch-Beilinson型过滤的合理等效性之间的各种联系，从而对Marian和Zhao的最新结果进行了普遍的解释。
We investigate the Lefschetz standard conjecture for degree $2$ cohomology of hyper-Kähler manifolds admitting a covering by Lagrangian subvarieties. In the case of a Lagrangian fibration, we show that the Lefschetz standard conjecture is implied by the SYZ conjecture characterizing classes of divisors associated with Lagrangian fibration. In dimension $4$, we consider the more general case of a Lagrangian covered fourfold $X$, and prove the Lefschetz standard conjecture in degree $2$, assuming $ρ(X)=1$ and $X$ is general in moduli. Finally we discuss various links between Lefschetz cycles and the study of the rational equivalence of points and Bloch-Beilinson type filtrations, giving a general interpretation of a recent intriguing result of Marian and Zhao.
