{"title":"On the leading constant in the Manin-type conjecture for Campana points","author":[{"full_name":"Shute, Alec L","last_name":"Shute","first_name":"Alec L","orcid":"0000-0002-1812-2810","id":"440EB050-F248-11E8-B48F-1D18A9856A87"}],"_id":"12077","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2104.14946","open_access":"1"}],"date_published":"2021-04-30T00:00:00Z","oa":1,"oa_version":"Preprint","type":"preprint","publication_status":"submitted","article_processing_charge":"No","language":[{"iso":"eng"}],"date_updated":"2023-02-21T16:37:30Z","article_number":"2104.14946","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2104.14946"]},"month":"04","day":"30","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"12072"}]},"year":"2021","department":[{"_id":"TiBr"}],"abstract":[{"text":"We compare the Manin-type conjecture for Campana points recently formulated\r\nby Pieropan, Smeets, Tanimoto and V\\'{a}rilly-Alvarado with an alternative\r\nprediction of Browning and Van Valckenborgh in the special case of the orbifold\r\n$(\\mathbb{P}^1,D)$, where $D =\\frac{1}{2}[0]+\\frac{1}{2}[1]+\\frac{1}{2}[\\infty]$. We find that the two predicted leading constants do not agree, and we discuss whether thin sets\r\ncould explain this discrepancy. Motivated by this, we provide a counterexample\r\nto the Manin-type conjecture for Campana points, by considering orbifolds\r\ncorresponding to squareful values of binary quadratic forms.","lang":"eng"}],"doi":"10.48550/arXiv.2104.14946","citation":{"short":"A.L. Shute, ArXiv (n.d.).","chicago":"Shute, Alec L. “On the Leading Constant in the Manin-Type Conjecture for Campana Points.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2104.14946\">https://doi.org/10.48550/arXiv.2104.14946</a>.","apa":"Shute, A. L. (n.d.). On the leading constant in the Manin-type conjecture for Campana points. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2104.14946\">https://doi.org/10.48550/arXiv.2104.14946</a>","ieee":"A. L. Shute, “On the leading constant in the Manin-type conjecture for Campana points,” <i>arXiv</i>. .","ama":"Shute AL. On the leading constant in the Manin-type conjecture for Campana points. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2104.14946\">10.48550/arXiv.2104.14946</a>","ista":"Shute AL. On the leading constant in the Manin-type conjecture for Campana points. arXiv, 2104.14946.","mla":"Shute, Alec L. “On the Leading Constant in the Manin-Type Conjecture for Campana Points.” <i>ArXiv</i>, 2104.14946, doi:<a href=\"https://doi.org/10.48550/arXiv.2104.14946\">10.48550/arXiv.2104.14946</a>."},"date_created":"2022-09-09T10:43:17Z","acknowledgement":"The author would like to thank Damaris Schindler and Florian Wilsch for their helpful comments on the heights and Tamagawa measures used in Section 3, together with Marta Pieropan, Sho Tanimoto and Sam Streeter for providing valuable feedback on an earlier version of this paper, and Tim Browning for many useful comments and discussions during the development of this work. The author is also grateful to the anonymous referee for providing many valuable comments and suggestions that improved the quality of the paper.","status":"public","publication":"arXiv"}