---
OA_place: publisher
OA_type: diamond
PlanS_conform: '1'
_id: '21244'
abstract:
- lang: eng
  text: 'Given a family of varieties over the projective line, we study the density
    of fibres that are everywhere locally soluble in the case that components of higher
    multiplicity are allowed. We use log geometry to formulate a new sparsity criterion
    for the existence of everywhere locally soluble fibres and formulate new conjectures
    that generalise previous work of Loughran and Smeets. These conjectures involve
    geometric invariants of the associated multiplicity orbifolds on the base of the
    fibration in the spirit of Campana. We give evidence for the conjectures by providing
    an assortment of bounds using Chebotarev’s theorem and sieve methods, with most
    of the evidence involving upper bounds. '
acknowledgement: We are very grateful to Tim Santens for useful conversations and
  to the anonymous referees for numerous pertinent remarks. While working on this
  paper, Browning was supported by a FWF grant (DOI 10.55776/P32428), Lyczak was supported
  by UKRI MR/V021362/1, and Smeets was supported by grant G0B1721N of the Fund for
  Scientific Research – Flanders.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
- first_name: Julian
  full_name: Lyczak, Julian
  last_name: Lyczak
- first_name: Arne
  full_name: Smeets, Arne
  last_name: Smeets
citation:
  ama: Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with
    multiple fibres. <i>Algebra &#38; Number Theory</i>. 2025;19(10):2049-2090. doi:<a
    href="https://doi.org/10.2140/ant.2025.19.2049">10.2140/ant.2025.19.2049</a>
  apa: Browning, T. D., Lyczak, J., &#38; Smeets, A. (2025). Paucity of rational points
    on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. Mathematical
    Sciences Publishers. <a href="https://doi.org/10.2140/ant.2025.19.2049">https://doi.org/10.2140/ant.2025.19.2049</a>
  chicago: Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational
    Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>.
    Mathematical Sciences Publishers, 2025. <a href="https://doi.org/10.2140/ant.2025.19.2049">https://doi.org/10.2140/ant.2025.19.2049</a>.
  ieee: T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations
    with multiple fibres,” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10. Mathematical
    Sciences Publishers, pp. 2049–2090, 2025.
  ista: Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations
    with multiple fibres. Algebra &#38; Number Theory. 19(10), 2049–2090.
  mla: Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with
    Multiple Fibres.” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10, Mathematical
    Sciences Publishers, 2025, pp. 2049–90, doi:<a href="https://doi.org/10.2140/ant.2025.19.2049">10.2140/ant.2025.19.2049</a>.
  short: T.D. Browning, J. Lyczak, A. Smeets, Algebra &#38; Number Theory 19 (2025)
    2049–2090.
corr_author: '1'
das_tickbox: '0'
date_created: 2026-02-16T15:22:19Z
date_published: 2025-09-05T00:00:00Z
date_updated: 2026-07-16T08:52:36Z
day: '05'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.2140/ant.2025.19.2049
external_id:
  arxiv:
  - '2310.01135'
file:
- access_level: open_access
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  creator: dernst
  date_created: 2026-02-17T11:56:20Z
  date_updated: 2026-02-17T11:56:20Z
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fulldoi: https://doi.org/10.2140/ant.2025.19.2049
has_accepted_license: '1'
intvolume: '        19'
issue: '10'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '09'
oa: 1
oa_version: Published Version
page: 2049-2090
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: Algebra & Number Theory
publication_identifier:
  eissn:
  - 1944-7833
  issn:
  - 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
researchdata_availability: no
status: public
supplementarymaterial: no
title: Paucity of rational points on fibrations with multiple fibres
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  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 19
year: '2025'
...