{"paper":{"title":"The first chiral homology group in higher genus","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Zuevsky","submitted_at":"2026-07-27T17:54:15Z","abstract_excerpt":"We extend the theory of the first chiral homology group of vertex algebras, developed by van\n  Ekeren and Heluani for elliptic curves, to compact Riemann surfaces of arbitrary genus. Our\n  approach realizes a genus $g$ surface by iterated self-sewing of $g$ handles onto the Riemann\n  sphere, each governed by a sewing parameter $\\rho_i$ in a punctured disc, so that the\n  construction of van Ekeren-Heluani is recovered.\n  We construct an explicit complex computing the chiral homology groups $H^{\\mathrm{ch}}_0$ and\n  $H^{\\mathrm{ch}}_1$ of a vertex algebra $V$ on a genus $g$ surface with $n$ mark"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24719","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/2607.24719/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"}