论文标题
具有指定本地行为的投影线上的Meromororphic连接
Meromorphic connections on the projective line with specified local behavior
论文作者
论文摘要
复杂的投影线上的Meromormormormormorphic连接在每个奇异点都会引起正式连接，这些正式连接构成了奇异性的局部行为。在这篇主要的说明论文中，我们讨论了在单数点上指定的局部行为的程度决定了全局联系。特别是，给定一组有限的要点和在这些点上的``正式类型''集合了，是否存在与这种局部行为的模态连接的模量空间？在本文中，我们讨论了这些问题的变体（例如，deligne--simpson和刚度问题），因为允许的奇异性变得越来越复杂：仅带有常规奇异性的第一个连接，接下来的连接允许额外的不符合不规则的奇异性，最后是一般案例。
A meromorphic connection on the complex projective line induces formal connections at each singular point, and these formal connections constitute the local behavior at the singularities. In this primarily expository paper, we discuss the extent to which specified local behavior at singular points determines the global connection. In particular, given a finite set of points and a collection of ``formal types'' at these points, does there exist a moduli space of meromorphic connections with this local behavior, and if so, when is this moduli space nonempty or a singleton? In this paper, we discuss variants of these problems (for example, the Deligne--Simpson and rigidity problems) as the allowed singularities get progressively more complicated: first connections with only regular singularities, next connections with additional unramified irregular singularities allowed, and finally the general case.
