{"paper":{"title":"Canonical systems and their limits on stable curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ziv Ran","submitted_at":"2011-04-25T16:36:40Z","abstract_excerpt":"We propose an object called 'sepcanonical system' on a stable curve $X_0$ which is to serve as limiting object- distinct from other such limits introduced previously- for the canonical system, as a smooth curve degenerates to $X_0$. First for curves which cannot be separated by 2 or fewer nodes, the so-called '2-inseparable' curves, the sepcanonical system is just the sections of the dualizing sheaf, which is not very ample iff $X_0$ is a limit of smooth hyperelliptic curves (such $X_0$ are called 2-inseparable hyperelliptics).\n  For general, 2-separable curves $X_0$ this assertion is false, l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4747","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"}