---
_id: '58185'
abstract:
- lang: eng
  text: "We consider a variant of the ring of components of Hurwitz spaces introduced\r\nby
    Ellenberg, Venkatesh and Westerland. By focusing on Hurwitz spaces\r\nclassifying
    covers of the projective line, the resulting ring of components is\r\ncommutative,
    which lets us study it from the point of view of algebraic\r\ngeometry and relate
    its geometric properties to numerical invariants involved\r\nin our previously
    obtained asymptotic counts. Specifically, we describe a\r\nstratification of the
    prime spectrum of the ring of components, and we compute\r\nthe dimensions and
    degrees of the strata. Using the stratification, we give a\r\ncomplete description
    of the spectrum in some cases."
author:
- first_name: Beranger Fabrice
  full_name: Seguin, Beranger Fabrice
  id: '102487'
  last_name: Seguin
citation:
  ama: Seguin BF. The Geometry of Rings of Components of Hurwitz Spaces. <i>arXiv:221012793</i>.
    Published online 2022.
  apa: Seguin, B. F. (2022). The Geometry of Rings of Components of Hurwitz Spaces.
    In <i>arXiv:2210.12793</i>.
  bibtex: '@article{Seguin_2022, title={The Geometry of Rings of Components of Hurwitz
    Spaces}, journal={arXiv:2210.12793}, author={Seguin, Beranger Fabrice}, year={2022}
    }'
  chicago: Seguin, Beranger Fabrice. “The Geometry of Rings of Components of Hurwitz
    Spaces.” <i>ArXiv:2210.12793</i>, 2022.
  ieee: B. F. Seguin, “The Geometry of Rings of Components of Hurwitz Spaces,” <i>arXiv:2210.12793</i>.
    2022.
  mla: Seguin, Beranger Fabrice. “The Geometry of Rings of Components of Hurwitz Spaces.”
    <i>ArXiv:2210.12793</i>, 2022.
  short: B.F. Seguin, ArXiv:2210.12793 (2022).
date_created: 2025-01-15T11:24:56Z
date_updated: 2025-01-15T11:35:43Z
external_id:
  arxiv:
  - '2210.12793'
language:
- iso: eng
publication: arXiv:2210.12793
status: public
title: The Geometry of Rings of Components of Hurwitz Spaces
type: preprint
user_id: '102487'
year: '2022'
...