---
_id: '10788'
abstract:
- lang: eng
  text: "We determine an asymptotic formula for the number of integral points of\r\nbounded
    height on a certain toric variety, which is incompatible with part of a\r\npreprint
    by Chambert-Loir and Tschinkel. We provide an alternative\r\ninterpretation of
    the asymptotic formula we get. To do so, we construct an\r\nanalogue of Peyre's
    constant $\\alpha$ and describe its relation to a new\r\nobstruction to the Zariski
    density of integral points in certain regions of\r\nvarieties."
acknowledgement: "Part of this work was conducted as a guest at the Institut de Mathématiques
  de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD.\r\nDuring
  this time, I had interesting and fruitful discussions on the interpretation of the
  result for\r\nthe toric variety discussed in Section 3 with Antoine Chambert-Loir.
  I wish to thank him for these\r\nopportunities and for his useful remarks on earlier
  versions of this article. This work was partly\r\nfunded by FWF grant P 32428-N35."
article_number: '2202.10909'
article_processing_charge: No
arxiv: 1
author:
- first_name: Florian Alexander
  full_name: Wilsch, Florian Alexander
  id: 560601DA-8D36-11E9-A136-7AC1E5697425
  last_name: Wilsch
  orcid: 0000-0001-7302-8256
citation:
  ama: Wilsch FA. Integral points of bounded height on a certain toric variety. <i>arXiv</i>.
    doi:<a href="https://doi.org/10.48550/arXiv.2202.10909">10.48550/arXiv.2202.10909</a>
  apa: Wilsch, F. A. (n.d.). Integral points of bounded height on a certain toric
    variety. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2202.10909">https://doi.org/10.48550/arXiv.2202.10909</a>
  chicago: Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain
    Toric Variety.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2202.10909">https://doi.org/10.48550/arXiv.2202.10909</a>.
  ieee: F. A. Wilsch, “Integral points of bounded height on a certain toric variety,”
    <i>arXiv</i>. .
  ista: Wilsch FA. Integral points of bounded height on a certain toric variety. arXiv,
    2202.10909.
  mla: Wilsch, Florian Alexander. “Integral Points of Bounded Height on a Certain
    Toric Variety.” <i>ArXiv</i>, 2202.10909, doi:<a href="https://doi.org/10.48550/arXiv.2202.10909">10.48550/arXiv.2202.10909</a>.
  short: F.A. Wilsch, ArXiv (n.d.).
date_created: 2022-02-23T09:04:43Z
date_published: 2022-02-22T00:00:00Z
date_updated: 2023-05-03T07:46:35Z
day: '22'
department:
- _id: TiBr
doi: 10.48550/arXiv.2202.10909
external_id:
  arxiv:
  - '2202.10909'
keyword:
- Integral point
- toric variety
- Manin's conjecture
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2202.10909
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: arXiv
publication_status: submitted
status: public
title: Integral points of bounded height on a certain toric variety
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_id: '10018'
abstract:
- lang: eng
  text: In order to study integral points of bounded log-anticanonical height on weak
    del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example,
    we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove
    an analogue of Manin's conjecture for integral points with respect to its singularities
    and its lines.
acknowledgement: The first author was partly supported by grant DE 1646/4-2 of the
  Deutsche Forschungsgemeinschaft. The second author was partly supported by FWF grant
  P 32428-N35 and conducted part of this work as a guest at the Institut de Mathématiques
  de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Ulrich
  full_name: Derenthal, Ulrich
  last_name: Derenthal
- first_name: Florian Alexander
  full_name: Wilsch, Florian Alexander
  id: 560601DA-8D36-11E9-A136-7AC1E5697425
  last_name: Wilsch
  orcid: 0000-0001-7302-8256
citation:
  ama: Derenthal U, Wilsch FA. Integral points on singular del Pezzo surfaces. <i>Journal
    of the Institute of Mathematics of Jussieu</i>. 2022. doi:<a href="https://doi.org/10.1017/S1474748022000482">10.1017/S1474748022000482</a>
  apa: Derenthal, U., &#38; Wilsch, F. A. (2022). Integral points on singular del
    Pezzo surfaces. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge
    University Press. <a href="https://doi.org/10.1017/S1474748022000482">https://doi.org/10.1017/S1474748022000482</a>
  chicago: Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular
    Del Pezzo Surfaces.” <i>Journal of the Institute of Mathematics of Jussieu</i>.
    Cambridge University Press, 2022. <a href="https://doi.org/10.1017/S1474748022000482">https://doi.org/10.1017/S1474748022000482</a>.
  ieee: U. Derenthal and F. A. Wilsch, “Integral points on singular del Pezzo surfaces,”
    <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University
    Press, 2022.
  ista: Derenthal U, Wilsch FA. 2022. Integral points on singular del Pezzo surfaces.
    Journal of the Institute of Mathematics of Jussieu.
  mla: Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular
    Del Pezzo Surfaces.” <i>Journal of the Institute of Mathematics of Jussieu</i>,
    Cambridge University Press, 2022, doi:<a href="https://doi.org/10.1017/S1474748022000482">10.1017/S1474748022000482</a>.
  short: U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu
    (2022).
date_created: 2021-09-15T10:06:48Z
date_published: 2022-11-10T00:00:00Z
date_updated: 2023-08-02T06:55:10Z
day: '10'
department:
- _id: TiBr
doi: 10.1017/S1474748022000482
external_id:
  arxiv:
  - '2109.06778'
  isi:
  - '000881319200001'
isi: 1
keyword:
- Integral points
- del Pezzo surface
- universal torsor
- Manin’s conjecture
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1017/S1474748022000482
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
  eissn:
  - '1475-3030 '
  issn:
  - 1474-7480
publication_status: epub_ahead
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Integral points on singular del Pezzo surfaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2022'
...