{"paper":{"title":"On Symplectic Coverings of the Projective Plane","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.SG","authors_text":"G.-M. Greuel, Vik.S. Kulikov","submitted_at":"2004-11-11T10:21:24Z","abstract_excerpt":"We prove that a resolution of singularities of any finite covering of the projective plane branched along a Hurwitz curve $\\bar H$ and, maybe, along a line \"at infinity\" can be embedded as a symplectic submanifold into some projective algebraic manifold equipped with an integer K\\\"{a}hler symplectic form (assuming that if $\\bar H$ has negative nodes, then the covering is non-singular over them). For cyclic coverings we can realize this embeddings into a rational algebraic 3--fold. Properties of the Alexander polynomial of $\\bar{H}$ are investigated and applied to the calculation of the first B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411253","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"}