{"paper":{"title":"On axioms of Frobenius like structure in the theory of arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.AG","authors_text":"Alexander Varchenko","submitted_at":"2016-01-10T12:29:13Z","abstract_excerpt":"A Frobenius manifold is a manifold with a flat metric and a Frobenius algebra structure on tangent spaces at points of the manifold such that the structure constants of multiplication are given by third derivatives of a potential function on the manifold with respect to flat coordinates.\n  In this paper we present a modification of that notion coming from the theory of arrangements of hyperplanes. Namely, given natural numbers $n>k$, we have a flat $n$-dimensional manifold and a vector space $V$ with a nondegenerate symmetric bilinear form and an algebra structure on $V$, depending on points o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02208","kind":"arxiv","version":3},"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"}