{"paper":{"title":"Symbolic powers of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Tony J. Puthenpurakal","submitted_at":"2019-08-06T11:30:28Z","abstract_excerpt":"Let $A = K[X_1,\\ldots, X_d]$ and let $I$, $J$ be monomial ideals in $A$. Let $I_n(J) = (I^n \\colon J^\\infty)$ be the $n^{th}$ symbolic power of $I$ \\wrt \\ $J$. It is easy to see that the function $f^I_J(n) = e_0(I_n(J)/I^n)$ is of quasi-polynomial type, say of period $g$ and degree $c$. For $n \\gg 0$ say \\[ f^I_J(n) = a_c(n)n^c + a_{c-1}(n)n^{c-1} + \\text{lower terms},\n  \\] where for $i = 0, \\ldots, c$, $a_i \\colon \\mathbb{N} \\rt \\mathbb{Z}$ are periodic functions of period $g$ and $a_c \\neq 0$.\n  In an earlier paper we (together with Herzog and Verma) proved that $\\dim I_n(J)/I^n$ is constant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02085","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02085/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}