{"paper":{"title":"On the number of intersection points of the contour of an amoeba with a line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Boris Shapiro, Eugenii Shustin, Lionel Lang","submitted_at":"2019-05-20T12:47:12Z","abstract_excerpt":"In this note, we investigate the maximal number of intersection points of a line with the contour of hypersurface amoebas in $\\mathbb{R}^n$. We define the latter number to be the $\\mathbb{R}$-degree of the contour. We also investigate the $\\mathbb{R}$-degree of related sets such as the boundary of amoebas and the amoeba of the real part of hypersurfaces defined over $\\mathbb{R}$. For all these objects, we provide bounds for the respective $\\mathbb{R}$-degrees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08056","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"}