{"paper":{"title":"The flat geometry of the $I_{1}$ singularity: $(x,y)\\mapsto(x,xy,y^{2},y^{3})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pedro Benedini Riul, Ra\\'ul Oset Sinha","submitted_at":"2018-04-27T16:44:13Z","abstract_excerpt":"We study the flat geometry of the least degenerate singularity of a singular surface in $\\mathbb R^4$, the $I_{1}$ singularity parametrised by $(x,y)\\mapsto(x,xy,y^{2},y^{3})$. This singularity appears generically when projecting a regular surface in $\\mathbb R^5$ orthogonally to $\\mathbb R^4$ along a tangent direction. We obtain a generic normal form for $I_1$ invariant under diffeomorphisms in the source and isometries in the target. We then consider the contact with hyperplanes by classifying submersions which preserve the image of $I_1$. The main tool is the study of the singularities of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11220","kind":"arxiv","version":1},"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"}