{"paper":{"title":"On Hurwitz--Severi numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Boris Shapiro, Yurii Burman","submitted_at":"2016-04-23T18:57:04Z","abstract_excerpt":"For a point $p\\in CP^2$ and a triple $(g,d,\\ell)$ of non-negative integers we define a {\\em Hurwitz--Severi number} ${\\mathfrak H}_{g,d,\\ell}$ as the number of generic irreducible plane curves of genus $g$ and degree $d+\\ell$ having an $\\ell$-fold node at $p$ and at most ordinary nodes as singularities at the other points, such that the projection of the curve from $p$ has a prescribed set of local and remote tangents and lines passing through nodes. In the cases $d+\\ell\\ge g+2$ and $d+2\\ell \\ge g+2 > d+\\ell$ we express the Hurwitz--Severi numbers via appropriate ordinary Hurwitz numbers. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06935","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"}