{"paper":{"title":"Algebro-geometric semistability of polarized toric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DG"],"primary_cat":"math.AG","authors_text":"Hajime Ono","submitted_at":"2010-09-01T04:20:53Z","abstract_excerpt":"Let $\\Delta\\subset \\mathbb{R}^n$ be an $n$-dimensional integral Delzant polytope. It is well-known that there exist the $n$-dimensional compact toric manifold $X_\\Delta$ and the very ample $(\\mathbb{C}^\\times)^n$-equivariant line bundle $L_\\Delta$ on $X_\\Delta$ associated with $\\Delta$. In the present paper, we give a necessary and sufficient condition for Chow semistability of $(X_\\Delta,L_\\Delta^i)$ for a maximal torus action. We then see that asymptotic (relative) Chow semistability implies (relative) K-semistability for toric degenerations, which is proved by Ross and Thomas, without any k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0087","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":""},"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"}