{"paper":{"title":"A new construction of $\\tilde{D}_5$-singularities and generalization of Slodowy slices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"K.Nakamoto, M.Tosun","submitted_at":"2012-09-25T08:45:48Z","abstract_excerpt":"Any simple elliptic singularity of type $\\tilde{D}_5$ can be obtained by taking the intersection of the nilpotent variety and the 4-dimensional \"good slices\" in the semi-simple Lie algebra ${\\frak sl}(2, {\\mathbb C}) \\oplus {\\frak sl}(2, {\\mathbb C})$. We describe these new slices purely by the structure of the Lie algebra. We also construct the semi-universal deformation spaces of $\\tilde{D}_5$-singularities by using the 4-dimensional \"good slices\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5541","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"}