{"paper":{"title":"Metrics of constant positive curvature with conical singularities, Hurwitz spaces, and ${\\rm det}\\, \\Delta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Alexey Kokotov, Victor Kalvin","submitted_at":"2016-12-27T15:40:17Z","abstract_excerpt":"Let $f: X\\to {\\Bbb C}P^1$ be a meromorphic function of degree $N$ with simple poles and simple critical points on a compact Riemann surface $X$ of genus $g$ and let $\\mathsf m$ be the standard round metric of curvature $1$ on the Riemann sphere ${\\Bbb C}P^1$. Then the pullback $f^*\\mathsf m$ of $\\mathsf m$ under $f$ is a metric of curvature $1$ with conical singularities of conical angles $4\\pi$ at the critical points of $f$. We study the $\\zeta$-regularized determinant of the Laplace operator on $X$ corresponding to the metric $f^*\\mathsf m$ as a functional on the moduli space of the pairs $("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08660","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"}