{"paper":{"title":"On the strong Lefschetz question for uniform powers of general linear forms in $k[x,y,z]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Juan Migliore, Rosa Mar\\'ia Mir\\'o-Roig","submitted_at":"2016-11-14T20:03:41Z","abstract_excerpt":"Schenck and Seceleanu proved that if $R = k[x,y,z]$, where $k$ is an infinite field, and $I$ is an ideal generated by any collection of powers of linear forms, then multiplication by a general linear form $L$ induces a homomorphism of maximal rank from any component of $R/I$ to the next. That is, $R/I$ has the {\\em weak Lefschetz property}. Considering the more general {\\em strong Lefschetz question} of when $\\times L^j$ has maximal rank for $j \\geq 2$, we give the first systematic study of this problem. We assume that the linear forms are general and that the powers are all the same, i.e. tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04544","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"}