{"paper":{"title":"Secant degeneracy index of the standard strata in the space of binary forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Boris Shapiro, Gleb Nenashev, Michael Shapiro","submitted_at":"2016-12-27T14:58:17Z","abstract_excerpt":"The space $Pol_d\\simeq \\bC P^d$ of all complex-valued binary forms of degree $d$ (considered up to a constant factor) has a standard stratification, each stratum of which contains all forms whose set of multiplicities of their distinct roots is given by a fixed partition $\\mu \\vdash d$. For each such stratum $S_\\mu,$ we introduce its secant degeneracy index $\\ell_\\mu$ which is the minimal number of projectively dependent pairwise distinct points on $S_\\mu$, i.e., points whose projective span has dimension smaller than $\\ell_\\mu-1$. In what follows, we discuss the secant degeneracy index $\\ell_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08651","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"}