{"paper":{"title":"Symplectic Torelli groups of rational surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GT"],"primary_cat":"math.SG","authors_text":"Jun Li, Tian-Jun Li, WeiWei Wu","submitted_at":"2022-12-04T16:57:10Z","abstract_excerpt":"We call a symplectic rational surface $(X,\\omega)$ \\textit{positive} if $c_1(X)\\cdot[\\omega]>0$. The positivity condition of a rational surface is equivalent to the existence of a divisor $D\\subset X$, such that $(X, D)$ is a log Calabi-Yau surface. The cohomology class of a symplectic form can be endowed with a \\textit{type} using the root system associated to its Lagrangian spherical classes. In this paper, we prove that the symplectic Torelli group of a positive rational surface is trivial if it is of type $\\mathbb{A}$, and is a sphere braid group if it is of type $\\mathbb{D}$.\n  As an appl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.01873","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.01873/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}