{"paper":{"title":"Uhlenbeck spaces via affine Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A.Braverman, D.Gaitsgory, M.Finkelberg","submitted_at":"2003-01-16T18:51:28Z","abstract_excerpt":"Let $G$ be an almost simple simply connected group over $\\BC$, and let $\\Bun^a_G(\\BP^2,\\BP^1)$ be the moduli scheme of principal $G$-bundles on the projective plave $\\BP^2$, of second Chern class $a$, trivialized along a line $\\BP^1\\subset \\BP^2$.\n  We define the Uhlenbeck compactification $\\fU^a_G$ of $\\Bun^a_G(\\BP^2,\\BP^1)$, which classifies, roughly, pairs $(\\F_G,D)$, where $D$ is a 0-cycle on $\\BA^2=\\BP^2-\\BP^1$ of degree $b$, and $\\F_G$ is a point of $\\Bun^{a-b}_G(\\BP^2,\\BP^1)$, for varying $b$.\n  In addition, we calculate the stalks of the Intersection Cohomology sheaf of $\\fU^a_G$. To d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301176","kind":"arxiv","version":4},"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"}