{"paper":{"title":"On the finiteness of loci of weighted plane curves in the moduli space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Monica Marinescu","submitted_at":"2018-03-21T16:23:12Z","abstract_excerpt":"For every fixed genus $g\\geq 1$, we consider all quadruples $Q=(w_0,w_1,w_2,d)\\in\\mathbb{Z}^4_{>0}$ with the property that any smooth degree-$d$ curve embedded in the weighted projective plane $\\mathbb{P}^2(w_0,w_1,w_2)$ has genus $g$. We show there are infinitely many quadruples $Q$ satisfying this condition. For every such $Q$, we consider $Z_Q\\subseteq M_g$ the locus in the moduli space of all smooth degree-$d$ curves embedded in $\\mathbb{P}^2(w_0,w_1,w_2)$. We show that, as $Q$ varies over all these quadruples, there are only finitely many different loci $Z_Q\\subseteq M_g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07992","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"}