{"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/contractibility-of-space-of-stability","title":"Contractibility of space of stability conditions on the projective plane via global dimension function","arxiv_id":"2001.11984","date":"2020-01-31","proceeding":null,"authors":["Yu-Wei Fan","Chunyi Li","Wanmin Liu","Yu Qiu"],"abstract":"We compute the global dimension function $\\mathrm{gldim}$ on the principal component $\\mathrm{Stab}^{\\dag}(\\mathbb{P}^2)$ of the space of Bridgeland stability conditions on $\\mathbb{P}^2$. It admits $2$ as the minimum value and the preimage $\\mathrm{gldim}^{-1}(2)$ is contained in the closure $\\bar{\\mathrm{Stab}^{\\mathrm{Geo}}(\\mathbb{P}^2)}$ of the subspace consisting of geometric stability conditions. We show that $\\mathrm{gldim}^{-1}[2,x)$ contracts to $\\mathrm{gldim}^{-1}(2)$ for any real number $x\\geq 2$ and that $\\mathrm{gldim}^{-1}(2)$ is contractible.","url_abs":"https://arxiv.org/abs/2001.11984v3","url_pdf":"https://arxiv.org/pdf/2001.11984v3.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":"contractibility-of-space-of-stability","repo_url":"https://github.com/wanminliu/wanminliu.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}