{"paper":{"title":"A correspondence of good G-sets under partial geometric quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Johannes Schmitt","submitted_at":"2016-11-09T14:52:50Z","abstract_excerpt":"For a complex variety $\\hat X$ with an action of a reductive group $\\hat G$ and a geometric quotient $\\pi: \\hat X \\to X$ by a closed normal subgroup $H \\subset \\hat G$, we show that open sets of $X$ admitting good quotients by $G=\\hat G / H$ correspond bijectively to open sets in $\\hat X$ with good $\\hat G$-quotients. We use this to compute GIT-chambers and their associated quotients for the diagonal action of $\\text{PGL}_2$ on $(\\mathbb{P}^1)^n$ in certain subcones of the $\\text{PGL}_2$-effective cone via a torus action on affine space. This allows us to represent these quotients as toric var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02958","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"}