{"paper":{"title":"Smooth mixed projective curves and a conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mutsuo Oka","submitted_at":"2017-11-27T05:08:09Z","abstract_excerpt":"Let $f(\\bf z,\\bar{\\bf z})$ be a strongly mixed homogeneous polynomial of 3 variables $\\bf z=(z_1,z_2,z_3)$ of polar degree $q$ with an isolated singularity at the origin. It defines a smooth Riemann surface $C$ in the complex projective space $\\mathbb P^2$. The fundamental group of the complement $\\mathbb P^2\\setminus C$ is cyclic group of order $q$ if $f$ is homogeneous polynomial without $\\bar{\\bf z}$. We propose a conjecture that this may be even true for mixed homogeneous polynomials by giving several supporting examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09537","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"}