{"paper":{"title":"Canonical blow-ups of Grassmannians I: How canonical is a Kausz compactification?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hanlong Fang, Xian Wu","submitted_at":"2024-11-16T10:00:34Z","abstract_excerpt":"In this paper, we develop a simple uniform picture incorporating the Kausz compactifications and the spaces of complete collineations by blowing up Grassmannians $G(p,n)$ according to a torus action $\\mathbb G_m$. We show that each space of complete collineations is isomorphic to any maximal-dimensional connected component of the $\\mathbb G_m$-fixed point scheme of a Kausz-type compactification. We prove that the Kausz-type compactification is the total family over the Hilbert quotient $G(p,n)/ \\! \\! / \\mathbb G_m$ which is isomorphic to the space of complete collineations. In particular, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10763","kind":"arxiv","version":2},"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/2411.10763/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"}