{"paper":{"title":"Universal Pl\\\"ucker coordinates for the Wronski map and positivity in real Schubert calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Kevin Purbhoo, Steven N. Karp","submitted_at":"2023-09-09T00:05:55Z","abstract_excerpt":"Given a $d$-dimensional vector space $V \\subset \\mathbb{C}[u]$ of polynomials, its Wronskian is the polynomial $(u + z_1) \\cdots (u + z_n)$ whose zeros $-z_i$ are the points of $\\mathbb{C}$ such that $V$ contains a nonzero polynomial with a zero of order at least $d$ at $-z_i$. Equivalently, $V$ is a solution to the Schubert problem defined by osculating planes to the moment curve at $z_1, \\dots, z_n$. The inverse Wronski problem involves finding all $V$ with a given Wronskian $(u + z_1) \\cdots (u + z_n)$. We solve this problem by providing explicit formulas for the Grassmann-Pl\\\"ucker coordin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04645","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.04645/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}