论文标题
在卡拉比Yau上计数表面4倍I：基础
Counting surfaces on Calabi-Yau 4-folds I: Foundations
论文作者
论文摘要
这是一系列关于计数卡拉比野4倍的表面的论文中的第一部分。除了二维亚化学的希尔伯特方案外，我们还介绍了稳定对的模量空间的\ emph {两种}类型。我们表明，这三个模量空间都通过git壁交叉和构成派生类别中的稳定对象进行参数化。 我们通过Kiem-Li Asection定位在模量空间上构建\ Emph {还原} OH-Thomas虚拟循环，并证明它们沿Hodge Loci沿Hodge Loci不变。作为一种应用，我们表明，任何支持非零的虚拟周期的hodge猜想都适用于任何4倍的卡拉比Yau家族。
This is the first part in a series of papers on counting surfaces on Calabi-Yau 4-folds. Besides the Hilbert scheme of 2-dimensional subschemes, we introduce \emph{two} types of moduli spaces of stable pairs. We show that all three moduli spaces are related by GIT wall-crossing and parametrize stable objects in the bounded derived category. We construct \emph{reduced} Oh-Thomas virtual cycles on the moduli spaces via Kiem-Li cosection localization and prove that they are deformation invariant along Hodge loci. As an application, we show that the variational Hodge conjecture holds for any family of Calabi-Yau 4-folds supporting a non-zero reduced virtual cycle.
