{"paper":{"title":"Construction of Maurer-Cartan elements over configuration spaces of curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Benjamin Enriquez, Federico Zerbini","submitted_at":"2021-10-18T14:09:45Z","abstract_excerpt":"For $C$ a complex curve and $n \\geq 1$, a pair $(\\mathcal{P},\\nabla_\\mathcal{P})$ of a principal bundle $\\mathcal{P}$ with meromorphic flat connection over $C^n$, holomorphic over the configuration space $C_n(C)$ of $n$ points over $C$, was introduced in arXiv:1112.0864. For any point $\\infty \\in C$, we construct a trivialisation of the restriction of $\\mathcal{P}$ to $(C\\setminus\\infty)^n$ and obtain a Maurer-Cartan element $J$ over $C_n(C\\setminus\\infty)$ out of $\\nabla_\\mathcal{P}$, thus generalising a construction of Levin and Racinet when the genus of $C$ is higher than one. We give expli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.09341","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/2110.09341/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"}