论文标题
Hyperkähler品种模量空间的Kodaira尺寸
Kodaira dimension of moduli spaces of hyperkähler varieties
论文作者
论文摘要
我们研究了偏振超喀勒品种变形的模量空间的kodaira尺寸，等效于K3表面上的Hilbert方案或O'Grady的十个维度品种。当$ k3^{[2]} $和OG10类型的情况下，Gritsenko-Hulek-Sankaran研究了这个问题。我们将它们的结果推广到更高的维度和分裂性。作为主要结果，对于几乎所有维度$ 2N $，我们提供了一个下限，以使所有较高程度，偏光hyperkähler品种$ k3^{[n]} $类型的模量空间的每个组件都是一般类型。
We study the Kodaira dimension of moduli spaces of polarized hyperkähler varieties deformation equivalent to the Hilbert scheme of points on a K3 surface or to O'Grady's ten dimensional variety. This question was studied by Gritsenko-Hulek-Sankaran in the cases of $K3^{[2]}$ and OG10 type when the divisibility of the polarization is one. We generalize their results to higher dimension and divisibility. As a main result, for almost all dimensions $2n$ we provide a lower bound on the degree such that for all higher degrees, every component of the moduli space of polarized hyperkähler varieties of $K3^{[n]}$ type is of general type.
