{"paper":{"title":"Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence","license":"","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.AC","authors_text":"Alexander I. Suciu, Henry K. Schenck","submitted_at":"2005-02-21T15:27:37Z","abstract_excerpt":"If \\A is a complex hyperplane arrangement, with complement X, we show that the Chen ranks of G=\\pi_1(X) are equal to the graded Betti numbers of the linear strand in a minimal, free resolution of the cohomology ring A=H^*(X,\\k), viewed as a module over the exterior algebra E on \\A: \\theta_k(G) = \\dim_\\k Tor^E_{k-1}(A,\\k)_k, where \\k is a field of characteristic 0, and k\\ge 2. The Chen ranks conjecture asserts that, for k sufficiently large, \\theta_k(G) =(k-1) \\sum_{r\\ge 1} h_r \\binom{r+k-1}{k}, where h_r is the number of r-dimensional components of the projective resonance variety R^1(\\A). Our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502438","kind":"arxiv","version":2},"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"}