Chow Rings of Hurwitz Spaces with Marked Ramification

2025/05/08 by Clader, Emily, Hu, Zhengning, Larson, Hannah +2
#14C15 #14C17 #14H10 #14H30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.04903

Abstract

The Hurwitz space \mathscrH_k,g is a compactification of the space of smooth genus-g curves with a simply-branched degree-k map to ℙ¹. In this paper, we initiate a study of the Chow rings of these spaces, proving in particular that when k=3 (which is the first case in which the Chow ring is not already known), the codimension-2 Chow group is generated by the fundamental classes of codimension-2 boundary strata. The key tool is to realize the codimension-1 boundary strata of \mathscrH_3,g as the images of gluing maps whose domains are products of Hurwitz spaces \mathscrH_k',g'(μ) with a single marked fiber of prescribed (not necessarily simple) ramification profile μ, and to prove that the spaces \mathscrH_k',g'(μ) with k'=2,3 have trivial Chow ring.

Citations

• The Integral Chow Ring of the Stack of Pointed Hyperelliptic Curves
• On the Chow and cohomology rings of moduli spaces of stable curves
• The integral Chow rings of the stacks of hyperelliptic Weierstrass points
• Chow rings of low-degree Hurwitz spaces
• Chow rings of stacks of prestable curves II
• The Hurwitz space Picard rank conjecture for d>g-1
• Twisted bundles and admissible covers

Related

• Chow rings of low-degree Hurwitz spaces
• On the Chow ring of the Hurwitz space of degree three covers of bf\n P¹
• Tautological classes on low-degree Hurwitz spaces
• Compactifications of Hurwitz spaces
• On a compactification of a Hurwitz space in the wild case