{"paper":{"title":"A few remarks on the Generalized Vanishing Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA"],"primary_cat":"math.AC","authors_text":"Michiel de Bondt","submitted_at":"2012-06-13T15:04:30Z","abstract_excerpt":"We show that the Generalized Vanishing Conjecture $$\\forall_{m \\ge 1} [\\Lam^m f^m = 0] \\Longrightarrow \\forall_{m \\gg 0} [\\Lam^m (g f^m) = 0]$$ for a fixed differential operator $\\Lam \\in k[\\partial]$ follows from a special case of it, namely that the additional factor $g$ is a power of the radical polynomial $f$. Next we show that in order to prove the Generalized Vanishing Conjecture (up to some bound on the degree of $\\Lam$), we may assume that $\\Lam$ is a linear combination of powers of distinct partial derivatives. At last, we show that the Generalized Vanishing Conjecture holds for produ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2836","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"}