{"paper":{"title":"Determinantal representation and subschemes of general plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Juan Migliore, Luca Chiantini","submitted_at":"2010-12-15T17:34:53Z","abstract_excerpt":"Let $M = (m_{ij})$ be an $n \\times n$ square matrix of integers. For our purposes, we can assume without loss of generality that $M$ is homogeneous and that the entries are non-increasing going leftward and downward. Let $d$ be the sum of the entries on either diagonal. We give a complete characterization of which such matrices have the property that a general form of degree $d$ in $\\mathbb C[x_0,x_1,x_2]$ can be written as the determinant of a matrix of forms $(f_{ij})$ with $\\deg f_{ij} = m_{ij}$ (of course $f_{ij} = 0$ if $m_{ij} < 0$). As a consequence, we answer the related question of wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3396","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"}