论文标题
标记和标记的Gushel-Mukai四倍
Marked and labelled Gushel-Mukai fourfolds
论文作者
论文摘要
我们证明，标记和标记的Hodge特殊Gushel-mukai四倍的模量是同构。作为一个应用程序，我们从Hodge特殊的Gushel-Mukai-Mukai四倍的判别$ d $构造了理性地图，以构建（扭曲）度-$ d $偏振的K3表面的模量空间。我们使用这些结果证明了一个计数公式，用于非常通用的Hodge特殊Gushel-Mukai-Mukai-Mukai四倍带有相关K3表面的4维纤维数量，在扭曲的相关K3表面的情况下，该数字的下限。
We prove that the moduli stacks of marked and labelled Hodge-special Gushel-Mukai fourfolds are isomorphic. As an application, we construct rational maps from the stack of Hodge-special Gushel-Mukai fourfolds of discriminant $d$ to the moduli space of (twisted) degree-$d$ polarized K3 surfaces. We use these results to prove a counting formula for the number of 4-dimensional fibers of Fourier-Mukai partners of very general Hodge-special Gushel-Mukai fourfolds with associated K3 surface, and a lower bound for this number in the case of a twisted associated K3 surface.
