{"paper":{"title":"On the shape of the K-semistable domain and wall crossing for K-stability","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chuyu Zhou","submitted_at":"2023-02-27T03:56:43Z","abstract_excerpt":"Fixing two positive integers $d$ and $k$, a positive number $v$, and a positive integer $I$, we prove that the K-semistable domain of the log pair $(X, \\sum_{j=1}^kD_j)$ is a rational polytope lying in the $k$-dimensional simplex $\\overline{\\Delta^k}$, where $X$ is a Fano variety of dimension $d$, $D_j\\sim_\\mathbb{Q} -K_X$, $(-K_X)^d=v$, $I(K_X+D_j)\\sim 0$, and $(X, \\sum_{j=1}^kc_jD_j)$ is a K-semistable log Fano pair for some $c_j\\in [0,1)\\cap \\mathbb{Q}$. Moreover, we show that there are only finitely many polytopes which may appear as the K-semistable domains for such log pairs. Based on th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.13503","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.13503/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}