[{"year":"2025","date_created":"2025-02-18T13:34:07Z","author":[{"id":"26ca6926-5797-11ee-9232-f8b51bd19631","full_name":"Faisant, Loïs","last_name":"Faisant","first_name":"Loïs"}],"language":[{"iso":"eng"}],"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"doi":"10.48550/ARXIV.2502.11704","oa":1,"publication_status":"submitted","ec_funded":1,"department":[{"_id":"TiBr"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"19055","researchdata_availability":"no","day":"17","OA_place":"repository","corr_author":"1","publication":"arXiv","title":"Motivic counting of rational curves with tangency conditions via universal torsors","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_processing_charge":"No","arxiv":1,"date_published":"2025-02-17T00:00:00Z","external_id":{"arxiv":["2502.11704"]},"date_updated":"2026-07-16T09:24:48Z","month":"02","oa_version":"Preprint","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."}],"citation":{"short":"L. Faisant, ArXiv (n.d.).","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>.","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>.","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>","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>","ieee":"L. Faisant, “Motivic counting of rational curves with tangency conditions via universal torsors,” <i>arXiv</i>. ."},"article_number":"2502.11704","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.11704","open_access":"1"}],"das_tickbox":"0","OA_type":"green","supplementarymaterial":"no","type":"preprint","status":"public"}]