{"paper":{"title":"Fiber cones, analytic spreads of the canonical and anticanonical ideals and limit Frobenius complexity of Hibi rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mitsuhiro Miyazaki","submitted_at":"2018-04-03T15:52:43Z","abstract_excerpt":"Let ${\\cal R}_{\\mathbb{K}}[H]$ be the Hibi ring over a field $\\mathbb{K}$ on a finite distributive lattice $H$, $P$ the set of join-irreducible elements of $H$ and $\\omega$ the canonical ideal of ${\\cal R}_{\\mathbb{K}}[H]$. We show the powers $\\omega^{(n)}$ of $\\omega$ in the group of divisors $\\mathrm{Div}({\\cal R}_{\\mathbb{K}}[H])$ is identical with the ordinal powers of $\\omega$, describe the $\\mathbb{K}$-vector space basis of $\\omega^{(n)}$ for $n\\in\\mathbb{Z}$. Further, we show that the fiber cones $\\bigoplus_{n\\geq 0}\\omega^n/\\mathfrak{m}\\omega^n$ and $\\bigoplus_{n\\geq0}(\\omega^{(-1)})^n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01046","kind":"arxiv","version":3},"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"}