---
_id: '11636'
abstract:
- lang: eng
  text: In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility
    theorems over an arbitrary field, based on random hyperplane slicing. In this
    paper, we extend their work by proving an analogous bound for the dimension of
    the exceptional locus in the setting of linear subspaces of higher codimensions.
article_number: '102085'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Philip
  full_name: Kmentt, Philip
  id: c90670c9-0bf0-11ed-86f5-ed522ece2fac
  last_name: Kmentt
- first_name: Alec L
  full_name: Shute, Alec L
  id: 440EB050-F248-11E8-B48F-1D18A9856A87
  last_name: Shute
  orcid: 0000-0002-1812-2810
citation:
  ama: Kmentt P, Shute AL. The Bertini irreducibility theorem for higher codimensional
    slices. <i>Finite Fields and their Applications</i>. 2022;83(10). doi:<a href="https://doi.org/10.1016/j.ffa.2022.102085">10.1016/j.ffa.2022.102085</a>
  apa: Kmentt, P., &#38; Shute, A. L. (2022). The Bertini irreducibility theorem for
    higher codimensional slices. <i>Finite Fields and Their Applications</i>. Elsevier.
    <a href="https://doi.org/10.1016/j.ffa.2022.102085">https://doi.org/10.1016/j.ffa.2022.102085</a>
  chicago: Kmentt, Philip, and Alec L Shute. “The Bertini Irreducibility Theorem for
    Higher Codimensional Slices.” <i>Finite Fields and Their Applications</i>. Elsevier,
    2022. <a href="https://doi.org/10.1016/j.ffa.2022.102085">https://doi.org/10.1016/j.ffa.2022.102085</a>.
  ieee: P. Kmentt and A. L. Shute, “The Bertini irreducibility theorem for higher
    codimensional slices,” <i>Finite Fields and their Applications</i>, vol. 83, no.
    10. Elsevier, 2022.
  ista: Kmentt P, Shute AL. 2022. The Bertini irreducibility theorem for higher codimensional
    slices. Finite Fields and their Applications. 83(10), 102085.
  mla: Kmentt, Philip, and Alec L. Shute. “The Bertini Irreducibility Theorem for
    Higher Codimensional Slices.” <i>Finite Fields and Their Applications</i>, vol.
    83, no. 10, 102085, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.ffa.2022.102085">10.1016/j.ffa.2022.102085</a>.
  short: P. Kmentt, A.L. Shute, Finite Fields and Their Applications 83 (2022).
date_created: 2022-07-24T22:01:41Z
date_published: 2022-10-01T00:00:00Z
date_updated: 2023-08-03T12:12:57Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1016/j.ffa.2022.102085
external_id:
  arxiv:
  - '2111.06697'
  isi:
  - '000835490600001'
file:
- access_level: open_access
  checksum: 3ca88decb1011180dc6de7e0862153e1
  content_type: application/pdf
  creator: dernst
  date_created: 2023-02-02T07:56:34Z
  date_updated: 2023-02-02T07:56:34Z
  file_id: '12475'
  file_name: 2022_FiniteFields_Kmentt.pdf
  file_size: 247615
  relation: main_file
  success: 1
file_date_updated: 2023-02-02T07:56:34Z
has_accepted_license: '1'
intvolume: '        83'
isi: 1
issue: '10'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
publication: Finite Fields and their Applications
publication_identifier:
  eissn:
  - '10902465'
  issn:
  - '10715797'
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Bertini irreducibility theorem for higher codimensional slices
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 83
year: '2022'
...