论文标题
准标记品种的基本组是环状基团的免费产品
Quasi-projective varieties whose fundamental group is a free product of cyclic groups
论文作者
论文摘要
在这项工作中，我们研究了光滑的复杂准四位方表面，其基本组是环状基团的免费产物。特别是，我们证明了从准标记表面到光滑复杂的准标记曲线的可允许图的存在。与该结果相关的是，我们证明了可允许地图的纤维的添加缺失引理，这些引理描述了这些操作如何影响准标准表面的基本组。我们的方法还使我们能够在光滑的投影表面中产生曲线，其补充的基本组是环状群体的免费产品，将经典结果推广到$ c_ {p，q} $曲线和圆环类型的投影式六文化，并显示了这种现象的一般性。
In this work we study smooth complex quasi-projective surfaces whose fundamental group is a free product of cyclic groups. In particular, we prove the existence of an admissible map from the quasi-projective surface to a smooth complex quasi-projective curve. Associated with this result, we prove addition-deletion Lemmas for fibers of the admissible map which describe how these operations affect the fundamental group of the quasi-projective surface. Our methods also allow us to produce curves in smooth projective surfaces whose fundamental groups of their complements are free products of cyclic groups, generalizing classical results on $C_{p,q}$ curves and torus type projective sextics, and showing how general this phenomenon is.
