---
_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: '9199'
abstract:
- lang: eng
  text: "We associate a certain tensor product lattice to any primitive integer lattice
    and ask about its typical shape. These lattices are related to the tangent bundle
    of Grassmannians and their study is motivated by Peyre's programme on \"freeness\"
    for rational points of bounded height on Fano\r\nvarieties."
acknowledgement: The authors are very grateful to Will Sawin for useful remarks about
  this topic. While working on this paper the first two authors were supported by
  EPSRC grant EP/P026710/1, and the first and last authors by FWF grant P 32428-N35.
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: Tal
  full_name: Horesh, Tal
  id: C8B7BF48-8D81-11E9-BCA9-F536E6697425
  last_name: Horesh
- 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: Browning TD, Horesh T, Wilsch FA. Equidistribution and freeness on Grassmannians.
    <i>Algebra &#38; Number Theory</i>. 2022;16(10):2385-2407. doi:<a href="https://doi.org/10.2140/ant.2022.16.2385">10.2140/ant.2022.16.2385</a>
  apa: Browning, T. D., Horesh, T., &#38; Wilsch, F. A. (2022). Equidistribution and
    freeness on Grassmannians. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences
    Publishers. <a href="https://doi.org/10.2140/ant.2022.16.2385">https://doi.org/10.2140/ant.2022.16.2385</a>
  chicago: Browning, Timothy D, Tal Horesh, and Florian Alexander Wilsch. “Equidistribution
    and Freeness on Grassmannians.” <i>Algebra &#38; Number Theory</i>. Mathematical
    Sciences Publishers, 2022. <a href="https://doi.org/10.2140/ant.2022.16.2385">https://doi.org/10.2140/ant.2022.16.2385</a>.
  ieee: T. D. Browning, T. Horesh, and F. A. Wilsch, “Equidistribution and freeness
    on Grassmannians,” <i>Algebra &#38; Number Theory</i>, vol. 16, no. 10. Mathematical
    Sciences Publishers, pp. 2385–2407, 2022.
  ista: Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians.
    Algebra &#38; Number Theory. 16(10), 2385–2407.
  mla: Browning, Timothy D., et al. “Equidistribution and Freeness on Grassmannians.”
    <i>Algebra &#38; Number Theory</i>, vol. 16, no. 10, Mathematical Sciences Publishers,
    2022, pp. 2385–407, doi:<a href="https://doi.org/10.2140/ant.2022.16.2385">10.2140/ant.2022.16.2385</a>.
  short: T.D. Browning, T. Horesh, F.A. Wilsch, Algebra &#38; Number Theory 16 (2022)
    2385–2407.
date_created: 2021-02-25T09:56:57Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-02T06:46:38Z
day: '01'
department:
- _id: TiBr
doi: 10.2140/ant.2022.16.2385
external_id:
  arxiv:
  - '2102.11552'
  isi:
  - '000961514100004'
intvolume: '        16'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2102.11552
month: '12'
oa: 1
oa_version: Preprint
page: 2385-2407
project:
- _id: 26A8D266-B435-11E9-9278-68D0E5697425
  grant_number: EP-P026710-2
  name: Between rational and integral points
- _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'
scopus_import: '1'
status: public
title: Equidistribution and freeness on Grassmannians
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 16
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'
...
---
_id: '12776'
abstract:
- lang: eng
  text: An improved asymptotic formula is established for the number of rational points
    of bounded height on the split smooth del Pezzo surface of degree 5. The proof
    uses the five conic bundle structures on the surface.
acknowledgement: This work was begun while the author was participating in the programme
  on "Diophantine equations" at the Hausdorff Research Institute for Mathematics in
  Bonn in 2009. The hospitality and financial support of the institute is gratefully
  acknowledged. The idea of using conic bundles to study the split del Pezzo surface
  of degree 5 was explained to the author by Professor Salberger. The author is very
  grateful to him for his input into this project and also to Shuntaro Yamagishi for
  many useful comments on an earlier version of this manuscript. While working on
  this paper the author was supported by FWF grant P32428-N35.
article_processing_charge: No
article_type: original
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
citation:
  ama: Browning TD. Revisiting the Manin–Peyre conjecture for the split del Pezzo
    surface of degree 5. <i>New York Journal of Mathematics</i>. 2022;28:1193-1229.
  apa: Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split
    del Pezzo surface of degree 5. <i>New York Journal of Mathematics</i>. State University
    of New York.
  chicago: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split
    Del Pezzo Surface of Degree 5.” <i>New York Journal of Mathematics</i>. State
    University of New York, 2022.
  ieee: T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo
    surface of degree 5,” <i>New York Journal of Mathematics</i>, vol. 28. State University
    of New York, pp. 1193–1229, 2022.
  ista: Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del
    Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.
  mla: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del
    Pezzo Surface of Degree 5.” <i>New York Journal of Mathematics</i>, vol. 28, State
    University of New York, 2022, pp. 1193–229.
  short: T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.
date_created: 2023-03-28T09:21:09Z
date_published: 2022-08-24T00:00:00Z
date_updated: 2023-10-18T07:59:13Z
day: '24'
ddc:
- '510'
department:
- _id: TiBr
file:
- access_level: open_access
  checksum: c01e8291794a1bdb7416aa103cb68ef8
  content_type: application/pdf
  creator: dernst
  date_created: 2023-03-30T07:09:35Z
  date_updated: 2023-03-30T07:09:35Z
  file_id: '12778'
  file_name: 2022_NYJM_Browning.pdf
  file_size: 897267
  relation: main_file
  success: 1
file_date_updated: 2023-03-30T07:09:35Z
has_accepted_license: '1'
intvolume: '        28'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 1193 - 1229
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: New York Journal of Mathematics
publication_identifier:
  issn:
  - 1076-9803
publication_status: published
publisher: State University of New York
quality_controlled: '1'
status: public
title: Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree
  5
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2022'
...
---
_id: '8742'
abstract:
- lang: eng
  text: We develop a version of Ekedahl’s geometric sieve for integral quadratic forms
    of rank at least five. As one ranges over the zeros of such quadratic forms, we
    use the sieve to compute the density of coprime values of polynomials, and furthermore,
    to address a question about local solubility in families of varieties parameterised
    by the zeros.
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: Roger
  full_name: Heath-Brown, Roger
  last_name: Heath-Brown
citation:
  ama: Browning TD, Heath-Brown R. The geometric sieve for quadrics. <i>Forum Mathematicum</i>.
    2021;33(1):147-165. doi:<a href="https://doi.org/10.1515/forum-2020-0074">10.1515/forum-2020-0074</a>
  apa: Browning, T. D., &#38; Heath-Brown, R. (2021). The geometric sieve for quadrics.
    <i>Forum Mathematicum</i>. De Gruyter. <a href="https://doi.org/10.1515/forum-2020-0074">https://doi.org/10.1515/forum-2020-0074</a>
  chicago: Browning, Timothy D, and Roger Heath-Brown. “The Geometric Sieve for Quadrics.”
    <i>Forum Mathematicum</i>. De Gruyter, 2021. <a href="https://doi.org/10.1515/forum-2020-0074">https://doi.org/10.1515/forum-2020-0074</a>.
  ieee: T. D. Browning and R. Heath-Brown, “The geometric sieve for quadrics,” <i>Forum
    Mathematicum</i>, vol. 33, no. 1. De Gruyter, pp. 147–165, 2021.
  ista: Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum
    Mathematicum. 33(1), 147–165.
  mla: Browning, Timothy D., and Roger Heath-Brown. “The Geometric Sieve for Quadrics.”
    <i>Forum Mathematicum</i>, vol. 33, no. 1, De Gruyter, 2021, pp. 147–65, doi:<a
    href="https://doi.org/10.1515/forum-2020-0074">10.1515/forum-2020-0074</a>.
  short: T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165.
date_created: 2020-11-08T23:01:25Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-10-17T07:39:01Z
day: '01'
department:
- _id: TiBr
doi: 10.1515/forum-2020-0074
external_id:
  arxiv:
  - '2003.09593'
  isi:
  - '000604750900008'
intvolume: '        33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2003.09593
month: '01'
oa: 1
oa_version: Preprint
page: 147-165
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: Forum Mathematicum
publication_identifier:
  eissn:
  - 1435-5337
  issn:
  - 0933-7741
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: The geometric sieve for quadrics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2021'
...