{"paper":{"title":"Definable Galois theory for bimeromorphic geometry","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.LO","authors_text":"Anand Pillay, Rahim Moosa","submitted_at":"2025-08-27T02:36:11Z","abstract_excerpt":"The outlines of a \"Galois theory\" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal meromorphic bundles with algebraic structure group, and admitting no horizontal subvarieties, is deduced. Examples of algebraic groups arising as binding groups are provided, as is a characterisation of when they are linear. Using binding groups in CCM it is shown that, in contrast to the situation in differentially closed fields, there are many algebraic grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.19524","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/2508.19524/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"}