{"paper":{"title":"Degeneration of differentials and 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":"A.L. Knutsen, C. Ciliberto, C. Galati, F. Flamini","submitted_at":"2017-01-25T09:40:10Z","abstract_excerpt":"We consider, under suitable assumptions, the following situation: $\\mathcal B$ is a component of the moduli space of polarized surfaces and $\\mathcal V_{m,\\delta}$ is the universal Severi variety over $\\mathcal B$ parametrizing pairs $(S,C)$, with $(S,H)\\in \\mathcal B$ and $C\\in |mH|$ irreducible with exactly $\\delta$ nodes as singularities. The moduli map $\\mathcal V\\to \\mathcal M_g$ of an irreducible component $\\mathcal V$ of $\\mathcal V_{m,\\delta}$ is generically of maximal rank if and only if certain cohomology vanishings hold. Assuming there are suitable semistable degenerations of the su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07224","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"}