{"paper":{"title":"On the classification of Togliatti systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Mart\\'i Salat, Rosa Maria Mir\\'o-Roig","submitted_at":"2017-10-07T17:18:22Z","abstract_excerpt":"In [MeMR], Mezzetti and Mir\\'{o}-Roig proved that the minimal number of generators $\\mu (I)$ of a minimal (smooth) monomial Togliatti system $I\\subset k[x_{0},\\dotsc,x_{n}]$ satisfies $2n+1\\le \\mu(I)\\le \\binom{n+d-1}{n-1}$ and they classify all smooth minimal monomial Togliatti systems $I\\subset k[x_{0},\\dotsc,x_{n}]$ with $2n+1\\le \\mu(I)\\le 2n+2$. In this paper, we address the first open case. We classify all smooth monomial Togliatti systems $I\\subset k[x_{0},\\dotsc,x_{n}]$ of forms of degree $d\\ge 4$ with $\\mu(I)=2n+3$ and $n\\ge 2$ and all monomial Togliatti systems $I\\subset k[x_0,x_1,x_2]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03579","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"}