{"paper":{"title":"An algebraic construction of a solution to the mean field equations on hyperelliptic Curves and its diabatic limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chih-Chun Liu, Jia-Ming Liou","submitted_at":"2017-05-24T14:36:47Z","abstract_excerpt":"In this paper, we give an algebraic construction of the solution to the following mean field equation $$ \\Delta \\psi+e^{\\psi}=4\\pi\\sum_{i=1}^{2g+2}\\delta_{P_{i}}, $$ on a genus $g\\geq 2$ hyperelliptic curve $(X,ds^{2})$ where $ds^{2}$ is a canonical metric on $X$ and $\\{P_{1},\\cdots,P_{2g+2}\\}$ is the set of Weierstrass points on $X.$ Furthermore, we study the rescaled equation $$ \\Delta \\psi+\\gamma e^{\\psi}=4\\pi\\gamma \\sum_{i=1}^{2g+2}\\delta_{P_{i}} $$ and its adiabatic limit at $\\gamma=0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08791","kind":"arxiv","version":4},"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"}