{"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/initial-degenerations-of-flag-varieties","title":"Initial degenerations of flag varieties","arxiv_id":"2207.08094","date":"2022-07-17","proceeding":null,"authors":["Daniel Corey","Jorge Alberto Olarte"],"abstract":"We prove that the initial degenerations of the flag variety admit closed immersions into finite inverse limits of flag matroid strata, where the diagrams are derived from matroidal subdivisions of a suitable flag matroid polytope. As an application, we prove that the initial degenerations of $\\operatorname{F\\ell}^{\\circ}(n)$ -- the open subvariety of the complete flag variety $\\operatorname{F\\ell}(n)$ consisting of flags in general position -- are smooth and irreducible when $n\\leq 4$. We also study the Chow quotient of $\\operatorname{F\\ell}(n)$ by the diagonal torus of $\\operatorname{PGL}(n)$, and show that, for $n=4$, this is a log crepant resolution of its log canonical model.","url_abs":"https://arxiv.org/abs/2207.08094v1","url_pdf":"https://arxiv.org/pdf/2207.08094v1.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":"initial-degenerations-of-flag-varieties","repo_url":"https://github.com/dcorey2814/initialdegenerationsflagvarieties","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","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}