论文标题
GALOIS封面的基本组$ 6 $表面
Fundamental group of Galois covers of degree $6$ surfaces
论文作者
论文摘要
在本文中，我们考虑了6度的代数表面的Galois覆盖物，并及所有相关的平面退化。我们使用它们的退化计算了这些Galois覆盖的基本组。我们表明，对于8种类型的退化，Galois覆盖物的基本组是不平凡的，而对于20种类型的类型是微不足道的。此外，我们通过这种类型的变性来计算所有表面的Chern数字，并证明其所有Galois封面的签名都是负面的。我们根据我们的发现制定了有关Galois覆盖的基本组的结构的猜想。作者的附录列出了详细计算和附录，通过对6度平面退化进行分类。
In this paper we consider the Galois covers of algebraic surfaces of degree 6, with all associated planar degenerations. We compute the fundamental groups of those Galois covers, using their degeneration. We show that for 8 types of degenerations the fundamental group of the Galois cover is non-trivial and for 20 types it is trivial. Moreover, we compute the Chern numbers of all the surfaces with this type of degeneration and prove that the signatures of all their Galois covers are negative. We formulate a conjecture regarding the structure of the fundamental groups of the Galois covers based on our findings. With an appendix by the authors listing the detailed computations and an appendix by Guo Zhiming classifying degree 6 planar degenerations.
