{"paper":{"title":"Mixed Hodge structures and Weierstrass $\\sigma$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Grzegorz Banaszak, Jan Milewski","submitted_at":"2012-11-04T14:38:29Z","abstract_excerpt":"A $\\sigma$-operator on a complexification $V_{\\C}$ of an $\\R$-vector space $V_{\\R}$ is an operator $A \\in \\rm{End}_{\\C} (V_{\\C})$ such that $\\sigma (A) = 0$ where $\\sigma (z)$ denotes the Weierstrass $\\sigma$-function. In this paper we define the notion of the strongly pseudo-real $\\sigma$-operator and prove that there is one to one correspondence between real mixed Hodge structures and strongly pseudo-real $\\sigma$-operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0687","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"}