{"paper":{"title":"Non-surjective Gaussian maps for singular curves on K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claudio Fontanari, Edoardo Sernesi","submitted_at":"2018-02-05T09:35:45Z","abstract_excerpt":"Let $(S,L)$ be a polarized K3 surface with $\\mathrm{Pic}(S) = \\mathbb{Z}[L]$ and $L\\cdot L=2g-2$, let $C$ be a nonsingular curve of genus $g-1$ and let $f:C\\to S$ be such that $f(C) \\in \\vert L \\vert$. We prove that the Gaussian map $\\Phi_{\\omega_C(-T)}$ is non-surjective, where $T$ is the degree two divisor over the singular point $x$ of $f(C)$. This generalizes a result of Kemeny with an entirely different proof. It uses the very ampleness of $C$ on the blown-up surface $\\widetilde S$ of $S$ at $x$ and a theorem of L'vovski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01311","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"}