论文标题
Hurwitz空间的组成部分的几何形状
The Geometry of Rings of Components of Hurwitz Spaces
论文作者
论文摘要
我们考虑了Ellenberg，Venkatesh和Westerland引入的Hurwitz空间组成部分的变体。通过关注射射线线的赫维兹空间分类的盖子，所得的组件环是交换性的，这使我们可以从代数几何形状的角度研究它，并将其几何特性与参与我们先前获得的渐进计数涉及的数值不变性相关联。具体而言，我们描述了组件环的序列的分层，并计算地层的尺寸和程度。在某些情况下，使用分层，我们对频谱进行完整描述。
We consider a variant of the ring of components of Hurwitz spaces introduced by Ellenberg, Venkatesh and Westerland. By focusing on Hurwitz spaces classifying covers of the projective line, the resulting ring of components is commutative, which lets us study it from the point of view of algebraic geometry and relate its geometric properties to numerical invariants involved in our previously obtained asymptotic counts. Specifically, we describe a stratification of the prime spectrum of the ring of components, and we compute the dimensions and degrees of the strata. Using the stratification, we give a complete description of the spectrum in some cases.
