Multiple Saddle Connections on Flat Surfaces and the Principal Boundry of the Moduli Spaces of Quadratic Differentials
Multiple Saddle Connections on Flat Surfaces and the Principal Boundry of the Moduli Spaces of Quadratic Differentials
复制标题
平面上的多重鞍连接与二次微分模空间的主界
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
A. Zorich
中科院分区：
文献类型：
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作者：
H. Masur;A. Zorich
摘要：我们刻画了二次微分的典型退化，从而刻画了至多具有简单极点的亚纯二次微分模空间的“一般尖点”。在涉及模空间紧致化信息的问题中，模空间边界的非“一般”退化部分通常是可以忽略的。然而，即使对于典型的退化，在Riemann曲面上也可能有几个同时收缩的短环。我们解释了这一现象，描述了短环的所有刚性构型，给出了这里出现的去奇异稳定曲线的类似的详细描述，并展示了如何重建具有二次微分的Riemann曲面，该二次微分靠近主边界上的对应点的“尖点”。
Abstract.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” from the corresponding point at the principal boundary.