{"paper":{"title":"Hilbert-Kunz density function and asymptotic Hilbert-Kunz multiplicity for projective toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Mandira Mondal, V. Trivedi","submitted_at":"2017-07-19T07:29:35Z","abstract_excerpt":"For a toric pair $(X, D)$, where $X$ is a projective toric variety of dimension $d-1\\geq 1$ and $D$ is a very ample $T$-Cartier divisor, we show that the Hilbert-Kunz density function $HKd(X, D)(\\lambda)$ is the $d-1$ dimensional volume of ${\\overline {\\mathcal P}}_D \\cap \\{z= \\lambda\\}$, where ${\\overline {\\mathcal P}}_D\\subset {\\mathbb R}^d$ is a compact $d$-dimensional set (which is a finite union of convex polytopes).\n  We also show that, for $k\\geq 1$, the function\n  $HKd(X, kD)$ can be replaced by another compactly supported continuous function $\\varphi_{kD}$ which is `linear in $k$'. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05959","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"}