---
OA_place: repository
OA_type: green
_id: '19055'
abstract:
- lang: eng
  text: "Using the formalism of Cox rings and universal torsors, we prove a decomposition
    of the Grothendieck motive of the moduli space of morphisms from an arbitrary
    smooth projective curve to a Mori Dream Space (MDS).\r\n For the simplest cases
    of MDS, that of toric varieties, we use this decomposition to prove an instance
    of the motivic Batyrev--Manin--Peyre principle for curves satisfying tangency
    conditions with respect to the boundary divisors, often called Campana curves."
acknowledgement: "The author acknowledges funding from the European Union’s Horizon
  2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement
  No 101034413.\r\n"
article_number: '2502.11704'
article_processing_charge: No
arxiv: 1
author:
- first_name: Loïs
  full_name: Faisant, Loïs
  id: 26ca6926-5797-11ee-9232-f8b51bd19631
  last_name: Faisant
citation:
  ama: Faisant L. Motivic counting of rational curves with tangency conditions via
    universal torsors. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/ARXIV.2502.11704">10.48550/ARXIV.2502.11704</a>
  apa: Faisant, L. (n.d.). Motivic counting of rational curves with tangency conditions
    via universal torsors. <i>arXiv</i>. <a href="https://doi.org/10.48550/ARXIV.2502.11704">https://doi.org/10.48550/ARXIV.2502.11704</a>
  chicago: Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions
    via Universal Torsors.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/ARXIV.2502.11704">https://doi.org/10.48550/ARXIV.2502.11704</a>.
  ieee: L. Faisant, “Motivic counting of rational curves with tangency conditions
    via universal torsors,” <i>arXiv</i>. .
  ista: Faisant L. Motivic counting of rational curves with tangency conditions via
    universal torsors. arXiv, 2502.11704.
  mla: Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions
    via Universal Torsors.” <i>ArXiv</i>, 2502.11704, doi:<a href="https://doi.org/10.48550/ARXIV.2502.11704">10.48550/ARXIV.2502.11704</a>.
  short: L. Faisant, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-02-18T13:34:07Z
date_published: 2025-02-17T00:00:00Z
date_updated: 2025-04-14T07:54:52Z
day: '17'
department:
- _id: TiBr
doi: 10.48550/ARXIV.2502.11704
ec_funded: 1
external_id:
  arxiv:
  - '2502.11704'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2502.11704
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: arXiv
publication_status: submitted
status: public
title: Motivic counting of rational curves with tangency conditions via universal
  torsors
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...