{"paper":{"title":"A construction of hyperk\\\"ahler metrics through Riemann-Hilbert problems I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"C\\'esar Garza","submitted_at":"2017-01-27T20:50:09Z","abstract_excerpt":"In 2009 Gaiotto, Moore and Neitzke presented a new construction of hyperk\\\"{a}hler metrics on the total spaces of certain complex integrable systems, represented as a torus fibration $\\mathcal{M}$ over a base space $\\mathcal{B}$, except for a divisor $D$ in $\\mathcal{B}$, in which the torus fiber degenerates into a nodal torus. The hyperk\\\"{a}hler metric $g$ is obtained via solutions $\\mathcal{X}_\\gamma$ of a Riemann-Hilbert problem. We interpret the Kontsevich-Soibelman Wall Crossing Formula as an isomonodromic deformation of a family of RH problems, therefore guaranteeing continuity of $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08188","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":""},"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"}