{"paper":{"title":"On the constancy regions for mixed test ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Felipe P\\'erez","submitted_at":"2012-08-25T18:34:49Z","abstract_excerpt":"In this note we study the partition of $\\mathbb{R}_{\\geq0}^{n}$ given by the regions where the mixed test ideals $\\tau(\\mathfrak{a}_{1}^{t_{1}}... \\mathfrak{a}_{n}^{t_{n}})$ are constant. We show that each region can be described as the preimage of a natural number under a p-fractal function $\\varphi:\\mathbb{R}_{\\geq0}^{n}\\rightarrow\\mathbb{N}$. In addition, we give some examples illustrating that these regions do not need to be composed of finitely many rational polytopes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5158","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"}