---
OA_place: repository
OA_type: green
_id: '19053'
abstract:
- lang: eng
  text: Building on previous works by Bilu, Chambert-Loir and Loeser, we study the
    asymptotic behaviour of the moduli space of sections of a given family over a
    smooth projective curve, assuming that the generic fiber is an equivariant compactification
    of a finite dimensional vector space. Working in a suitable Grothendieck ring
    of varieties, we show that the class of these moduli spaces converges, modulo
    an adequate normalisation, to a non-zero effective element, when the class of
    the sections goes arbitrary far from the boundary of the dual of the effective
    cone. The limit can be interpreted as a motivic Euler product in the sense of
    Bilu’s thesis. This result provides a positive answer to a motivic version of
    the Batyrev–Manin–Peyre conjectures in this particular setting.
acknowledgement: I am grateful to Emmanuel Peyre for his help, reading and useful
  comments throughout the drafting process of this article. I am also very indebted
  to Margaret Bilu for all the constructions and properties that I used in this paper
  and which are due to her, especially those concerning the motivic Euler product,
  as well as for enlightening discussions and remarks on an earlier version of this
  work. I thank the anonymous referee for his/her remarks and suggestions that helped
  me to enhance the clarity of the exposition.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Loïs
  full_name: Faisant, Loïs
  id: 26ca6926-5797-11ee-9232-f8b51bd19631
  last_name: Faisant
citation:
  ama: Faisant L. Geometric Batyrev–Manin–Peyre for equivariant compactifications
    of additive groups. <i>Beiträge zur Algebra und Geometrie / Contributions to Algebra
    and Geometry</i>. 2023;64(3):783-850. doi:<a href="https://doi.org/10.1007/s13366-022-00656-w">10.1007/s13366-022-00656-w</a>
  apa: Faisant, L. (2023). Geometric Batyrev–Manin–Peyre for equivariant compactifications
    of additive groups. <i>Beiträge Zur Algebra Und Geometrie / Contributions to Algebra
    and Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s13366-022-00656-w">https://doi.org/10.1007/s13366-022-00656-w</a>
  chicago: Faisant, Loïs. “Geometric Batyrev–Manin–Peyre for Equivariant Compactifications
    of Additive Groups.” <i>Beiträge Zur Algebra Und Geometrie / Contributions to
    Algebra and Geometry</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s13366-022-00656-w">https://doi.org/10.1007/s13366-022-00656-w</a>.
  ieee: L. Faisant, “Geometric Batyrev–Manin–Peyre for equivariant compactifications
    of additive groups,” <i>Beiträge zur Algebra und Geometrie / Contributions to
    Algebra and Geometry</i>, vol. 64, no. 3. Springer Nature, pp. 783–850, 2023.
  ista: Faisant L. 2023. Geometric Batyrev–Manin–Peyre for equivariant compactifications
    of additive groups. Beiträge zur Algebra und Geometrie / Contributions to Algebra
    and Geometry. 64(3), 783–850.
  mla: Faisant, Loïs. “Geometric Batyrev–Manin–Peyre for Equivariant Compactifications
    of Additive Groups.” <i>Beiträge Zur Algebra Und Geometrie / Contributions to
    Algebra and Geometry</i>, vol. 64, no. 3, Springer Nature, 2023, pp. 783–850,
    doi:<a href="https://doi.org/10.1007/s13366-022-00656-w">10.1007/s13366-022-00656-w</a>.
  short: L. Faisant, Beiträge Zur Algebra Und Geometrie / Contributions to Algebra
    and Geometry 64 (2023) 783–850.
date_created: 2025-02-18T13:32:39Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2025-02-24T10:50:30Z
day: '01'
doi: 10.1007/s13366-022-00656-w
extern: '1'
external_id:
  arxiv:
  - '2106.11898'
intvolume: '        64'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2106.11898'
month: '09'
oa: 1
oa_version: Preprint
page: 783-850
publication: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
publication_identifier:
  eissn:
  - 2191-0383
  issn:
  - 0138-4821
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Geometric Batyrev–Manin–Peyre for equivariant compactifications of additive
  groups
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 64
year: '2023'
...