{"paper":{"title":"Birational geometry of blowups via Weyl chamber decompositions and actions on curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Elisa Postinghel, Luis Jos\\'e Santana S\\'anchez, Maria Chiara Brambilla, Olivia Dumitrescu","submitted_at":"2024-10-23T16:34:09Z","abstract_excerpt":"We study the birational geometry of $X^n_s$, the blow-up of $\\mathbb{P}^n_\\mathbb{C}$ at $s$ points in general position. We identify a set of subvarieties, which we call Weyl $r$-planes, that belong to an orbit for the action of the Weyl group on $r$-cycles. They satisfy the following properties: they appear as stable base locus of divisors; each Weyl $r$-plane is swept out by an $(n-r)$-moving curve class; moreover, if $s\\ge n+3$, for any fixed $r$ all these curve classes belong to the same orbit for the Weyl action.\n  For Mori dream spaces of type $X^n_s$, all such orbits are finite and they"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18008","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.18008/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}