{"paper":{"title":"Automorphisms of unstable ${\\mathbb P}^1$-bundles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J\\'anos Koll\\'ar","submitted_at":"2024-05-28T14:08:25Z","abstract_excerpt":"Let $P\\to X$ be a ${\\mathbb P}^1$-bundle over a variety $X$. The aim of this note is to understand all connected, algebraic groups $$ \\operatorname{Aut}^\\circ(P)\\subset G\\subset \\operatorname{Bir}( X\\times {\\mathbb P}^1). $$ We get a quite complete answer if $\\operatorname{Aut}^\\circ(X)$ is a maximal, connected, algebraic subgroup of $\\operatorname{Bir}(X)$, and $P$ is sufficiently unstable.\n  This gives examples of connected, algebraic subgroups of $\\operatorname{Bir}({\\mathbb P}^4)$ that are not contained in any maximal one.\n  Version 2: references updated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.18201","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/2405.18201/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"}