{"paper":{"title":"Finite subgroups of $\\operatorname{PGL}_2(K)$ arising from configurations of skew lines in $\\mathbb{P}^3_K$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.GR"],"primary_cat":"math.AG","authors_text":"Giuseppe Favacchio","submitted_at":"2025-12-22T19:03:20Z","abstract_excerpt":"We study finite groups arising from configurations of pairwise skew lines in $\\mathbb{P}^3_K$. To such a configuration ${L}$ one associates a group $G_{L}\\subset \\mathrm{PGL}_2(K)$ acting on each line, and we investigate which finite subgroups of $\\mathrm{PGL}_2(K)$ can occur in this way.\n  Our main tool is a matrix description of skew lines in $\\mathbb{P}^3_K$, which gives explicit generators for $G_{L}$ in terms of matrices in $\\mathrm{GL}_2(K)$. In the abelian case, we prove that the relevant matrices are simultaneously upper triangular and obtain explicit families realizing cyclic groups a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.19811","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/2512.19811/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"}