{"paper":{"title":"Deforming a canonical curve inside a quadric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eduard Looijenga, Marco Boggi","submitted_at":"2017-02-02T18:14:35Z","abstract_excerpt":"Let $C\\subset{\\mathbb P}^{g-1}$ be a canonically embedded nonsingular nonhyperelliptic curve of genus $g$ and let $X\\subset{\\mathbb P}^{g-1}$ be a quadric containing $C$. Our main result states among other things that the Hilbert scheme of $X$ is at $[C\\subset X]$ a local complete intersection of dimension $g^2-1$, and is smooth when $X$ is. It also includes the assertion that the minimal obstruction space for this deformation problem is in fact the full associated $\\operatorname{Ext}^1$-group and that in particular the deformations of $C$ in $X$ are obstructed in case $C$ meets the singular l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00770","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"}