论文标题
关于Enriques表面的非分类不变的计算视图
A computational view on the non-degeneracy invariant for Enriques surfaces
论文作者
论文摘要
对于Enriques Surface $ s $，非偏差不变$ \ mathrm {nd}（s）$保留了$ S $及其极化的椭圆纤维纤维的信息。在当前的论文中，我们引入了非代理版的组合版本，该版本依赖于$ s $以及平滑的理性曲线的配置，并为$ \ mathrm {nd}（s）$提供了下限。我们提供了一个计算此组合不变的SageMath代码，并将其应用于几个示例。首先，我们确定一个新的Nodal Enriques表面，满足$ \ Mathrm {nd}（s）= 10 $，它不是通用的，并且与无限的自动形态组。我们在$ \ mathrm {nd}（s）$上获得了下界，以通过Mendes Lopes-pardini研究的八个不相交的平滑理性曲线。最后，我们恢复了Dolgachev和Kondō对具有有限的自动形态组的Enriques表面不变的计算，并提供了有关其椭圆纤维的几何形状的其他信息。
For an Enriques surface $S$, the non-degeneracy invariant $\mathrm{nd}(S)$ retains information on the elliptic fibrations of $S$ and its polarizations. In the current paper, we introduce a combinatorial version of the non-degeneracy invariant which depends on $S$ together with a configuration of smooth rational curves, and gives a lower bound for $\mathrm{nd}(S)$. We provide a SageMath code that computes this combinatorial invariant and we apply it in several examples. First we identify a new family of nodal Enriques surfaces satisfying $\mathrm{nd}(S)=10$ which are not general and with infinite automorphism group. We obtain lower bounds on $\mathrm{nd}(S)$ for the Enriques surfaces with eight disjoint smooth rational curves studied by Mendes Lopes-Pardini. Finally, we recover Dolgachev and Kondō's computation of the non-degeneracy invariant of the Enriques surfaces with finite automorphism group and provide additional information on the geometry of their elliptic fibrations.
