{"arxiv":1,"oa_version":"Preprint","author":[{"id":"26ca6926-5797-11ee-9232-f8b51bd19631","full_name":"Faisant, Loïs","first_name":"Loïs","last_name":"Faisant"}],"oa":1,"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."}],"publication":"arXiv","department":[{"_id":"TiBr"}],"language":[{"iso":"eng"}],"month":"02","status":"public","article_number":"2502.11704","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2025-02-17T00:00:00Z","citation":{"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>","short":"L. Faisant, ArXiv (n.d.).","ista":"Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv, 2502.11704.","ieee":"L. Faisant, “Motivic counting of rational curves with tangency conditions via universal torsors,” <i>arXiv</i>. .","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>.","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>."},"day":"17","article_processing_charge":"No","corr_author":"1","date_updated":"2025-04-14T07:54:52Z","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","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"OA_place":"repository","title":"Motivic counting of rational curves with tangency conditions via universal torsors","external_id":{"arxiv":["2502.11704"]},"ec_funded":1,"doi":"10.48550/ARXIV.2502.11704","year":"2025","publication_status":"submitted","_id":"19055","OA_type":"green","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.11704","open_access":"1"}],"date_created":"2025-02-18T13:34:07Z"}