{"paper":{"title":"Comparison of K\\\"{a}hler quotients of torus actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.AG","authors_text":"Xiangdong Yang, Xiangsheng Wang","submitted_at":"2026-07-07T14:45:09Z","abstract_excerpt":"Let $T$ be a torus with the complexification $T^{\\mathbb{C}}$ and $(X, ds^{2})$ a compact K\\\"{a}hler Hamiltonian $T$-manifold with the moment map $\\Phi$ such that $T^{\\mathbb{C}}$ acts on $X$ holomorphically. For each $\\alpha$ in the moment body $\\Phi(X)$, the K\\\"{a}hler quotient $X_{\\alpha}=\\Phi^{-1}(\\alpha)/T$ is a reduced normal complex analytic space admitting a unique K\\\"{a}hler structure $\\kappa_{\\alpha}$ induced from $ds^{2}$. Inspired by the theory of variation of Geometric Invariant Theory, when $\\alpha$ moves from a subpolytope (a connected component of the set of regular values of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06345","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06345/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"}