2006/09/04 by Fu Liu, Liu, Fu, Brian Osserman +1
Mathematics · #05A15 #14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CO #msc:05A15 #msc:14H10
paper · pdf · doi:10.48550/arxiv.math/0609118
18 pages
arxiv created 2006/09/04 · openalex publication_date 2006/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study "pure-cycle" Hurwitz spaces, parametrizing covers of the projective line having only one ramified point over each branch point. We start with the case of genus-0 covers, using a combination of limit linear series theory and group theory to show that these spaces are always irreducible. In the case of four branch points, we also compute the associated Hurwitz numbers. Finally, we give a conditional result in the higher-genus case, requiring at least 3g simply branched points. These results have equivalent formulations in group theory, and in this setting complement results of Conway-Fried-Parker-Volklein.