平面上的多重鞍形连接与二次微分模空间的主边界
Multiple Saddle Connections on Flat Surfaces and Principal Boundary of the Moduli Spaces of Quadratic Differentials
摘要：
我们描述了典型的退化的二次微分，从而描述了“通用尖点”的模空间的亚纯二次微分至多单极点。在涉及模空间的紧化信息的问题中，不是由"一般“退化引起的那部分模空间的边界常常可以忽略不计。然而，即使对于一个典型的退化，在黎曼曲面上也可能有几个同时收缩的短环。我们解释这种现象，描述所有刚性配置的短循环，提出了一个详细的描述类似物的desingularized稳定曲线在这里产生的，并显示如何可以重建一个黎曼曲面赋予了二次微分，这是接近一个"尖点“的相应点在主边界。
英文摘要：
We describe typical degenerations of quadratic differentials thus describing ``generic cusps'' of the moduli space of meromorphic quadratic differentials with at most simple poles. The part of the boundary of the moduli space which does not arise from ``generic'' degenerations is often negligible in problems involving information on compactification of the moduli space. However, even for a typical degeneration one may have several short loops on the Riemann surface which shrink simultaneously. We explain this phenomenon, describe all rigid configurations of short loops, present a detailed description of analogs of desingularized stable curves arising here, and show how one can reconstruct a Riemann surface endowed with a quadratic differential which is close to a ``cusp'' by the corresponding point at the principal boundary.
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