论文标题
通过精确差分的地层闭合双分支基因座
The closure of double ramification loci via strata of exact differentials
论文作者
论文摘要
双重分辨率基因座，也称为$ 0 $ - 不同的地层，是平滑曲线的Moduli空间的代数亚变化，参数化riemann表面，因此存在一个合理的功能，规定的后果超过$ 0 $ $ $ \ f infty $。我们用几何学术语描述了双重分析基因座在Deligne-Mumford紧凑型内部的关闭。 为了一个合理的函数，我们将其确切的差异关联，这使我们能够将双重分析基因座视为Meromormormorphic差异层的线性亚变化。然后，我们使用我们最近在线性亚变化边界的结果获得了封闭的几何描述。我们的方法产生了一种新的方式，可以将理性函数基因座和Teichmüller动力学的几何形状联系起来。我们还使用可允许的封面将结果与另一种方法进行比较。
Double ramification loci, also known as strata of $0$-differentials, are algebraic subvarieties of the moduli space of smooth curves parametrizing Riemann surfaces such that there exists a rational function with prescribed ramification over $0$ and $\infty$. We describe the closure of double ramification loci inside the Deligne-Mumford compactification in geometric terms. To a rational function we associate its exact differential, which allows us to realize double ramification loci as linear subvarieties of strata of meromorphic differentials. We then obtain a geometric description of the closure using our recent results on the boundary of linear subvarieties. Our approach yields a new way of relating the geometry of loci of rational functions and Teichmüller dynamics. We also compare our results to a different approach using admissible covers.
