{"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/explicit-equations-of-the-fake-projective-1","title":"Explicit equations of the fake projective plane $(a=7,p=2,\\emptyset,D_3 X_7)$","arxiv_id":"2308.14237","date":"2023-08-28","proceeding":null,"authors":["Lev Borisov","Mattie Ji","Yanxin Li"],"abstract":"We find explicit equations of the fake projective plane $(a=7,p=2,\\emptyset,D_3 X_7)$, which lies in the same class as the fake projective plane $(a=7,p=2,\\emptyset,D_3 2_7)$ with $21$ automorphisms whose equations were previously found by Borisov and Keum. The method involves finding a birational model of a common Galois cover of these two surfaces.","url_abs":"https://arxiv.org/abs/2308.14237v1","url_pdf":"https://arxiv.org/pdf/2308.14237v1.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":"explicit-equations-of-the-fake-projective-1","repo_url":"https://github.com/mattie-ji/fpp-a7-p2-emptyset-d3-x7","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}