{"paper":{"title":"Reflection maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G. Pe\\~nafort-Sanchis","submitted_at":"2016-09-11T22:06:48Z","abstract_excerpt":"Given a reflection group $G$ acting on a complex vector space $V$, a reflection map is the composition of an embedding $X \\hookrightarrow V$ with the orbit map $V\\to\\mathbb C^p$ that maps a $G$-orbit to a point. Reflection maps can be very singular, but we give tools to study them easily. We find obstructions to $\\mathcal A$-stability of reflection maps and produce, in the unobstructed cases, infinite families of $\\mathcal A$-finite map-germs of any corank. We also relate them to conjectures of L\\^e, Mond and Ruas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03222","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":""},"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"}