{"paper":{"title":"Gr\\\"obner Bases of Generic Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Juliane Capaverde, Shuhong Gao","submitted_at":"2017-11-14T20:55:21Z","abstract_excerpt":"Let $I = ( f_1, \\dots, f_n )$ be a homogeneous ideal in the polynomial ring $K[x_1, \\dots,x_n]$ over a field $K$ generated by generic polynomials. Using an incremental approach based on a method by Gao, Guan and Volny, and properties of the standard monomials of generic ideals, we show how a Gr\\\"obner basis for the ideal $(f_1, \\dots, f_i)$ can be obtained from that of $(f_1, \\dots, f_{i-1})$. If $deg f_i = d_i$, we are able to give a complete description of the initial ideal of $I$ in the case where $d_i \\geq \\left(\\sum_{j=1}^{i-1}d_j\\right) - i -1$. It was conjectured by Moreno-Soc\\'ias that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05309","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"}