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.

中文翻译：

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6 次曲面的伽罗瓦覆盖的基本群

在本文中，我们考虑了 6 次代数曲面的伽罗瓦覆盖，以及所有相关的平面退化。我们使用它们的退化来计算这些伽罗瓦覆盖的基本群。我们表明，对于 8 种类型的退化，伽罗瓦覆盖的基本群是非平凡的，而对于 20 种类型它是平凡的。此外，我们计算了所有具有这种退化的表面的陈数，并证明了它们所有的伽罗瓦覆盖的签名都是负的。根据我们的发现，我们对伽罗瓦覆盖的基本群的结构提出了一个猜想。