{"paper":{"title":"Moduli of nodal curves on K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andreas Leopold Knutsen, Ciro Ciliberto, Concettina Galati, Flaminio Flamini","submitted_at":"2015-02-25T21:47:32Z","abstract_excerpt":"We consider modular properties of nodal curves on general $K3$ surfaces. Let $\\mathcal{K}_p$ be the moduli space of primitively polarized $K3$ surfaces $(S,L)$ of genus $p\\geqslant 3$ and $\\mathcal{V}_{p,m,\\delta}\\to \\mathcal{K}_p$ be the universal Severi variety of $\\delta$--nodal irreducible curves in $|mL|$ on $(S,L)\\in \\mathcal{K}_p$. We find conditions on $p, m,\\delta$ for the existence of an irreducible component $\\mathcal{V}$ of $\\mathcal{V}_{p,m,\\delta}$ on which the moduli map $\\psi: \\mathcal{V}\\to \\mathcal{M}_g$ (with $g= m^2 (p -1) + 1-\\delta$) has generically maximal rank different"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07378","kind":"arxiv","version":3},"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"}