{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/extreme-divisors-on-bar-m-07-and-differences","title":"Extreme Divisors on $\\bar{M}_{0,7}$ and Differences over Characteristic 2","arxiv_id":"2203.13917","date":"2022-03-25","proceeding":null,"authors":["Mathieu Dutour Sikirić","Eric Jovinelly"],"abstract":"We find 101,052 new extreme divisors on $\\bar{M}_{0,7}$ (in 31 $S_7$-orbits) and millions of extreme nef curves over characteristic 0. Over characteristic 2, we identify two more $S_7$-orbits of extreme divisors, and prove $\\bar{\\text{Eff}}^k (\\bar{M}_{0,n})$ is strictly larger over characteristic 2 than it is over characteristic 0, for all $1\\leq k \\leq n-6$. For each such $k$ we provide explicit cycles which are extreme in $\\text{Eff}^k(\\bar{M}_{0,n})$ over characteristic 2 but external to $\\bar{\\text{Eff}}^k(\\bar{M}_{0,n})$ over characteristic 0. We apply our method of finding new extreme divisors to compute $\\text{Eff}(\\bar{M}_{0,\\mathcal{A}})$ for $\\mathcal{A}=(\\frac{1}{3}, \\frac{1}{3}, \\frac{1}{3}, \\frac{1}{3}, \\frac{1}{3}, \\frac{1}{3}, 1)$, proving it is polyhedral over any field, and conjecture a description of $\\text{Eff}(\\text{Bl}_e \\bar{LM}_7)$.","url_abs":"https://arxiv.org/abs/2203.13917v1","url_pdf":"https://arxiv.org/pdf/2203.13917v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"extreme-divisors-on-bar-m-07-and-differences","repo_url":"https://github.com/ericjovinelly/m07algorithms","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}