{"paper":{"title":"The symmetric square of a curve and the Petri map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Bruno, E. Sernesi","submitted_at":"2011-06-16T10:12:59Z","abstract_excerpt":"Let $\\M_g$ be the course moduli space of complex projective nonsingular curves of genus $g$. We prove that when the Brill-Noether number $\\rho(g,1,n)$ is non-negative the Petri locus $P^1_{g,n}\\subset \\M_g$ has a divisorial component whose closure has a non-empty intersection with $\\Delta_0$. In order to prove the result we show that the scheme $G^1_n(\\Gamma)$ that parametrizes degree $n$ pencils on a curve $\\Gamma$ is isomorphic to a component of the Hilbert scheme parametrizing certain curves on the symmetric square $\\Gamma_2$ of $\\Gamma$ and we study the properties of such a family of curve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3190","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"}