论文标题
二维球的分支覆盖物空间的细胞结构
A cell structure of the space of branched coverings of the two-dimensional sphere
论文作者
论文摘要
对于封闭式的表面$σ$，$ x_ {σ，n} $是同构的空间，以保留$ n $ n $ fold的分支覆盖物$σ\ rightarrow s^2 $的二维领域。 At a previous paper, the authors constructed a compactification $\bar{X}_{Σ,n}$ of the space that coincides with the Diaz-Edidin-Natanzon-Turaev compactification of the Hurwitz space $H(Σ,n)\subset X_{Σ,n}$ consisting of isomorphism classes of branched coverings with all critical values being simple.使用Grothendieck的Dessins d'Enfants，我们构建了紧凑型的细胞结构。所获得的结果应用于海布鲁克表面上三角曲线的空间。
For a closed oriented surface $ Σ$ let $X_{Σ,n}$ be the space of isomorphism classes of orientation preserving $n$-fold branched coverings $ Σ\rightarrow S^2 $ of the two-dimensional sphere. At a previous paper, the authors constructed a compactification $\bar{X}_{Σ,n}$ of the space that coincides with the Diaz-Edidin-Natanzon-Turaev compactification of the Hurwitz space $H(Σ,n)\subset X_{Σ,n}$ consisting of isomorphism classes of branched coverings with all critical values being simple. Using Grothendieck's dessins d'enfants we construct a cell structure of the compactification. The obtained results are applied to the space of trigonal curves on a Hirzebruch surface.
