{"paper":{"title":"The homotopy type of spaces of resultants of bounded multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andrzej Kozlowski, Kohhei Yamaguchi","submitted_at":"2016-12-20T18:25:40Z","abstract_excerpt":"For positive integers $m,n, d\\geq 1$ with $(m,n)\\not= (1,1)$ and a field $\\Bbb F$ with its algebraic closure $\\overline{\\Bbb F}$, let $\\text{Poly}^{d,m}_n(\\Bbb F)$ denote the space of all $m$-tuples $(f_1(z),\\cdots ,f_m(z))\\in \\Bbb F [z]$ of monic polynomials of the same degree $d$ such that polynomials $f_1(z),\\cdots ,f_m(z)$ have no common root in $\\overline{\\Bbb F}$ of multiplicity $\\geq n$. These spaces were defined by Farb and Wolfson in \\cite{FW} as generalizations of spaces first studied by Arnold, Vassiliev, Segal and others in different contexts. In \\cite{FW} they obtained algebraic g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06793","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"}