{"paper":{"title":"Joyce structures from quadratic differentials on the sphere","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.DG","authors_text":"Timothy Moy","submitted_at":"2025-09-05T17:33:50Z","abstract_excerpt":"Motivated by known examples of Joyce structures on spaces of meromorphic quadratic differentials, we consider the isomonodromic deformations of particular second-order linear ODEs with rational potential. We show the infinitesimal isomonodromic deformations are the kernel of a closed $2$-form arising from the intersection pairing of an algebraic curve defined by the potential. This observation enables us to construct Joyce structures on a class of moduli spaces of meromorphic quadratic differentials on the Riemann sphere, and provides a new, geometric description of the hyper-K\\\"ahler structur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05275","kind":"arxiv","version":2},"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/2509.05275/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"}