{"paper":{"title":"Rigidification of holomorphic germs with non-invertible differential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Matteo Ruggiero","submitted_at":"2009-11-20T11:59:53Z","abstract_excerpt":"We study holomorphic germs $f:(\\mathbb{C}^2, 0) \\rightarrow (\\mathbb{C}^2,0) with non-invertible differential $df_0$. In order to do this, we search for a modification $\\pi:X \\rightarrow (\\mathbb{C}^2,0)$ (i.e., a composition of point blow-ups over the origin), and an infinitely near point $p \\in \\pi^{-1}(0)$, such that the germ $f$ lifts to a holomorphic germ $\\hat{f}:(X,p) \\rightarrow (X,p)$ which is rigid (i.e., the generalized critical set of $\\hat{f}$ is totally invariant and has normal crossings at $p$). We extend a previous result for superattracting germs to the general case, and deal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4023","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":""},"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"}