{"paper":{"title":"The Enumerative Geometry of Hyperplane Arrangements","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Max Wakefield, Thomas Paul, Will Traves","submitted_at":"2014-09-22T18:47:10Z","abstract_excerpt":"We study enumerative questions on the moduli space $\\mathcal{M}(L)$ of hyperplane arrangements with a given intersection lattice $L$. Mn\\\"ev's universality theorem suggests that these moduli spaces can be arbitrarily complicated; indeed it is even difficult to compute the dimension $D =\\dim \\mathcal{M}(L)$. Embedding $\\mathcal{M}(L)$ in a product of projective spaces, we study the degree $N=\\mathrm{deg} \\mathcal{M}(L)$, which can be interpreted as the number of arrangements in $\\mathcal{M}(L)$ that pass through $D$ points in general position. For generic arrangements $N$ can be computed combin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6275","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"}