{"paper":{"title":"On the rigidity of moduli of weighted pointed stable curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex Massarenti, Barbara Fantechi","submitted_at":"2017-01-20T17:08:36Z","abstract_excerpt":"Let $\\overline{\\mathcal{M}}_{g,A[n]}$ be the Hassett moduli stack of weighted stable curves, and let $\\overline{M}_{g,A[n]}$ be its coarse moduli space. These are compactifications of $\\mathcal{M}_{g,n}$ and $M_{g,n}$ respectively, obtained by assigning rational weights $A = (a_{1},...,a_{n})$, $0< a_{i} \\leq 1$ to the markings; they are defined over $\\mathbb{Z}$, and therefore over any field. We study the first order infinitesimal deformations of $\\overline{\\mathcal{M}}_{g,A[n]}$ and $\\overline{M}_{g,A[n]}$. In particular, we show that $\\overline{M}_{0,A[n]}$ is rigid over any field, if $g\\ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05861","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"}