{"paper":{"title":"Analogues of hyperlogarithm functions on affine complex 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":"2022-12-06T16:31:42Z","abstract_excerpt":"For $C$ a smooth affine complex curve, there is a unique minimal subalgebra $A_C$ of the algebra $\\mathcal O_{hol}(\\tilde C)$ of holomorphic functions on its universal cover $\\tilde C$, which is stable under all the operations $f\\mapsto \\int f\\omega$, for $\\omega$ in the space $\\Omega(C)$ of regular differentials on $C$. We identify $A_C$ with the image of the iterated integration map $I_{x_0} : \\mathrm{Sh}(\\Omega(C))\\to\\mathcal O_{hol}(\\tilde C)$ based at any point $x_0$ of $\\tilde C$ (here $\\mathrm{Sh}(-)$ denotes the shuffle algebra of a vector space), as well as with the unipotent part, wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.03119","kind":"arxiv","version":3},"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/2212.03119/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"}