{"paper":{"title":"New and old results on spherical varieties via moduli theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Roman Avdeev, St\\'ephanie Cupit-Foutou","submitted_at":"2015-08-02T18:02:48Z","abstract_excerpt":"Given a connected reductive algebraic group $G$ and a finitely generated monoid $\\Gamma$ of dominant weights of $G$, in 2005 Alexeev and Brion constructed a moduli scheme $\\mathrm M_\\Gamma$ for multiplicity-free affine $G$-varieties with weight monoid $\\Gamma$. This scheme is equipped with an action of an `adjoint torus' $T_{\\mathrm{ad}}$ and has a distinguished $T_{\\mathrm{ad}}$-fixed point $X_0$. In this paper, we obtain a complete description of the $T_{\\mathrm{ad}}$-module structure in the tangent space of $\\mathrm M_\\Gamma$ at $X_0$ for the case where $\\Gamma$ is saturated. Using this des"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00268","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"}