{"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/failure-of-bott-vanishing-for-co-adjoint","title":"Failure of Bott vanishing for (co)adjoint partial flag varieties","arxiv_id":"2506.09811","date":"2025-06-11","proceeding":null,"authors":["Pieter Belmans"],"abstract":"Bott vanishing is a strong vanishing result for the cohomology of exterior powers of the cotangent bundle twisted by ample line bundles. Buch-Thomsen-Lauritzen-Mehta conjectured that partial flag varieties (which are not products of projective spaces) do not satisfy Bott vanishing, despite all their other nice properties. The cominuscule case is an easy application of the Borel-Weil-Bott theorem, following results of Snow. We show that the (co)adjoint partial flag varieties of all classical and exceptional Dynkin types also do not satisfy Bott vanishing, thus confirming the conjecture for this class of varieties.","url_abs":"https://arxiv.org/abs/2506.09811v1","url_pdf":"https://arxiv.org/pdf/2506.09811v1.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":"failure-of-bott-vanishing-for-co-adjoint","repo_url":"https://github.com/pbelmans/bott-non-vanishing","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}