The Noether-Lefschetz conjecture and generalizations
The Noether-Lefschetz conjecture and generalizations
复制标题
DOI：
10.1007/s00222-016-0695-z
复制
发表时间：
2014-12
影响因子：
3.1
通讯作者：
N. Bergeron;Zhiyuan Li;J. Millson;C. Moeglin
中科院分区：
文献类型：
--
作者：
N. Bergeron;Zhiyuan Li;J. Millson;C. Moeglin
证明了拟极化K3曲面模空间上的Noether-Lefschetz猜想。这是作为一般定理的一个特例推导出来的，该定理指出正交型算术流形的低阶上同调类与特殊循环类（即相同类型的子算术流形）是对偶的。对于紧流形，这在[3]中得到了证明，本文将[3]的结果推广到非紧流形。这使我们能够将我们的结果应用于准极化K3曲面的模空间。
We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal type are dual to the classes of special cycles, i.e. sub-arithmetic manifolds of the same type. For compact manifolds this was proved in [3], here we extend the results of [3] to non-compact manifolds. This allows us to apply our results to the moduli spaces of quasi-polarized K3 surfaces.