论文标题
椭圆形K3表面的某些模量空间的Kodaira尺寸
The Kodaira dimension of some moduli spaces of elliptic K3 surfaces
论文作者
论文摘要
我们研究了PICARD编号的椭圆形K3表面的模量空间，至少3，即$ u \ oplus \ langle -2K \ rangle $ polarlized k3表面。事实证明，这种模量空间是$ k \ geq 220 $的通用类型。证明依赖于Gritsenko，Hulek和Sankaran开发的低重量风口尖式的技巧。此外，某些椭圆形K3表面的显式几何结构导致这些模量空间的不合理性，$ k <11 $，对于其他19个隔离值，最高$ k = 64 $。
We study the moduli spaces of elliptic K3 surfaces of Picard number at least 3, i.e. $U\oplus \langle -2k \rangle$-polarized K3 surfaces. Such moduli spaces are proved to be of general type for $k\geq 220$. The proof relies on the low-weight cusp form trick developed by Gritsenko, Hulek and Sankaran. Furthermore, explicit geometric constructions of some elliptic K3 surfaces lead to the unirationality of these moduli spaces for $k < 11$ and for 19 other isolated values up to $k=64$.
