{"paper":{"title":"Divisors over determinantal rings defined by two by two minors","license":"","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin","submitted_at":"2006-08-14T14:10:51Z","abstract_excerpt":"Let E and G be free modules of rank e and g, respectively, over a commutative noetherian ring R. The identity map on E^* tensor G induces the Koszul complex\n ... -> S_mE^* tensor S_nG tensor Wedge^p(E^* tensor G) -> S_{m+1}E^* tensor S_{n+1}G tensor Wedge^{p-1}(E^* tensor G) -> ... and its dual\n ... -> D_{m+1}E tensor D_{n+1}G^* tensor Wedge^{p-1}(E tensor G^*) -> D_mE tensor D_nG^* tensor Wedge^p(E tensor G^*)-> ... Let H_{m,n,p} be the homology of the top complex at S_m tensor S_n tensor Wedge^p and H^{m,n,p} the homology of the bottom complex at D_m tensor D_n tensor Wedge^p. It is known th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608345","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"}