{"paper":{"title":"Rate and syzigies of modules over Veronese subrings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Rasoul Ahangari Maleki","submitted_at":"2014-10-29T13:09:18Z","abstract_excerpt":"Let $K$ be a field, $R$ be a standard graded $K$-algebra and $M$ be a finitely generated graded $R$-module. The rate of $M$, $\\rate_R(M)$, is a measure of the growth of the shifts in the minimal graded free resolution of $M$.\n  In this paper, we study the rate of Veronese modules of $M$. More precisely, it is shown that\n  $\\rate_{R^{(c)}}(M)\\leq \\lceil \\max\\{\\rate_{R}(M),\\rat(R)\\}/c\\rceil+\\max\\{0,\\lceil t^{R}_{0}(M)/c\\rceil\\},$ for all $c\\geq\n  1$. This extends a result of Herzog et al.\n  As a consequence of this, if $M$ is generated in degree zero, then $\\reg_{R^{(c)}}(M)=0$, for all\n  $c\\geq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7965","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"}