{"paper":{"title":"A Borel-Weil Theorem for Schur Modules","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Peter Magyar","submitted_at":"1994-11-21T22:44:45Z","abstract_excerpt":"We present a generalization of the classical Schur modules of $GL(N)$ exhibiting the same interplay among algebra, geometry, and combinatorics. A generalized Young diagram $D$ is an arbitrary finite subset of $\\NN \\times \\NN$.  For each $D$, we define the Schur module $S_D$ of $GL(N)$. We introduce a projective variety $\\FF_D$ and a line bundle $\\LL_D$, and describe the Schur module in terms of sections of $\\LL_D$.  For diagrams with the ``northeast'' property,\n  $$(i_1,j_1),\\ (i_2, j_2) \\in D  \\to (\\min(i_1,i_2),\\max(j_1,j_2)) \\in D ,$$\n which includes the skew diagrams, we resolve the singul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9411014","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"}