论文标题
复杂的双曲线轨道和Lefschetz纤维
Complex hyperbolic orbifolds and Lefschetz fibrations
论文作者
论文摘要
在PU（2,1）中，Hirzebruch和其他人在线路排列方面重新解释了PU（2,1）中的一类复杂的双曲线晶格。他们使用分支的盖子在适当地吹出射影2空间中线的四边形布置，以构建与晶格相关的Orbifolds上的复杂双曲线表面。 这些格子的基本领域是由帕斯奎内利（Pasquinelli）建造的。在这里，我们展示了如何以上面的线条安排来解释基本领域。然后在两个上下文中应用此平行。 Dashyan使用Hirzebruch的结构来构建无限的3个Manifolds表示。在这里，我们表明他的构造可以推广到所有Deligne-Mostow Lattices，并可以构建更多的表示。 韦尔斯表明，PU（2,1）中的两个Deligne-Mostow晶格可以看作是PU（1,1）中晶格的杂种。在这里，我们证明他隐含地使用了线条安排，并将他的分析完成到所有可能的线上。通过这种方式，我们表明可以将另外三个Deligne-Mostow Lattices作为混合动力。
A class of complex hyperbolic lattices in PU(2,1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch and others in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in projective 2-space to construct the complex hyperbolic surfaces over the orbifolds associated to the lattices. Fundamental domains for these lattices have been built by Pasquinelli. Here we show how the fundamental domains can be interpreted in terms of line arrangements as above. This parallel is then applied in two contexts. Dashyan uses Hirzebruch's construction to build infinitely many representations of 3-manifolds. Here we show that his construction can be generalised to all of the Deligne-Mostow lattices and more representations can be built. Wells shows that two of the Deligne-Mostow lattices in PU(2,1) can be seen as hybrids of lattices in PU(1,1). Here we show that he implicitly uses the line arrangement and we complete his analysis to all possible pairs of lines. In this way, we show that three more Deligne-Mostow lattices can be given as hybrids.
