{"paper":{"title":"Linear ind-Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alexander S. Tikhomirov, Ivan Penkov","submitted_at":"2013-10-30T07:57:18Z","abstract_excerpt":"We consider ind-varieties obtained as direct limits of chains of embeddings $X_1\\stackrel{\\phi_1}{\\hookrightarrow}\\dots\\stackrel{\\phi_{m-1}}{\\hookrightarrow} X_m\\stackrel{\\phi_m}{\\hookrightarrow}X_{m+1}\\stackrel{\\phi_{m+1}}{\\hookrightarrow}\\dots$, where each $X_m$ is a Grassmannian or an isotropic Grassmannian (possibly mixing Grassmannians and isotropic Grassmannians), and the embeddings $\\phi_m$ are linear in the sense that they induce isomorphisms of Picard groups. We prove that any such ind-variety is isomorphic to one of certain standard ind-Grassmannians and that the latter are pairwise "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8054","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"}