{"paper":{"title":"Log smoothness and polystability over valuation rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gaku Liu, Igor Pak, Karim Adiprasito, Michael Temkin","submitted_at":"2018-06-24T15:46:13Z","abstract_excerpt":"Let $\\mathcal{O}$ be a valuation ring of height one of residual characteristic exponent $p$ and with algebraically closed field of fractions. Our main result provides a best possible resolution of the monoidal structure $M_X$ of a log variety $X$ over $\\calO$ with a vertical log structure: there exists a log modification $Y\\to X$ such that the monoidal structure of $Y$ is polystable. In particular, if $X$ is log smooth over $\\mathcal{O}$, then $Y$ is polystable with a smooth generic fiber. As a corollary we deduce that any variety over $\\mathcal{O}$ possesses a polystable alteration of degreee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09168","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"}