{"paper":{"title":"Geometry and Singularities of Prony varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gil Goldman, Yehonatan Salman, Yosef Yomdin","submitted_at":"2018-06-05T14:03:23Z","abstract_excerpt":"We start a systematic study of the topology, geometry and singularities of the Prony varieties $S_q(\\mu)$, defined by the first $q+1$ equations of the classical Prony system\n  $$\\sum_{j=1}^d a_j x_j^k = \\mu_k, \\ k= 0,1,\\ldots \\ .$$ Prony varieties, being a generalization of the Vandermonde varieties, introduced in [5,21], present a significant independent mathematical interest (compare [5,19,21]). The importance of Prony varieties in the study of the error amplification patterns in solving Prony system was shown in [1-4,19]. In [19] a survey of these results was given, from the point of view o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02204","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"}