For the Galois closure $\Xgal$ of a generic projection from a surface $X$, itis believed that $\pi_1(\Xgal)$ gives rise to new invariants of $X$. However,in all examples this group is surprisingly simple. In this article, we offer anexplanation for this phenomenon: We compute a quotient of $\pi_1(\Xgal)$ thatdepends on $\pi_1(X)$ and data from the generic projection only. In all knownexamples except one, this quotient is in fact isomorphic to $\pi_1(\Xgal)$. Asa byproduct, we simplify part of the computations of Moishezon, Teicher andothers.
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机译：对于从表面$ X $进行的通用投影的Galois封闭$ \ Xgal $，艾蒂斯认为$ \ pi_1（\ Xgal）$会产生$ X $的新不变量。但是，在所有示例中，该组都非常简单。在本文中，我们对这种现象进行了解释：我们计算$ \ pi_1（\ Xgal）$的商，该商取决于$ \ pi_1（X）$和仅来自通用投影的数据。在除一个以外的所有已知示例中，该商实际上与$ \ pi_1（\ Xgal）$同构。作为副产品，我们简化了Moishezon，Teicher等人的部分计算。
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