{"paper":{"title":"Amoebas of genus at most one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Thorsten Theobald, Timo de Wolff","submitted_at":"2011-08-11T16:39:14Z","abstract_excerpt":"The amoeba of a Laurent polynomial $f \\in \\C[z_1^{\\pm 1},\\ldots,z_n^{\\pm 1}]$ is the image of its zero set $\\mathcal{V}(f)$ under the log-absolute-value map. Understanding the space of amoebas (i.e., the decomposition of the space of all polynomials, say, with given support or Newton polytope, with regard to the existing complement components) is a widely open problem.\n  In this paper we investigate the class of polynomials $f$ whose Newton polytope $\\New(f)$ is a simplex and whose support $A$ contains exactly one point in the interior of $\\New(f)$. Amoebas of polynomials in this class may hav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2456","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"}