{"paper":{"title":"Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jinsung Park, Lee-Peng Teo, Leon A. Takhtajan","submitted_at":"2015-08-10T00:50:47Z","abstract_excerpt":"For the TZ metric on the moduli space $\\mathscr{M}_{0,n}$ of $n$-pointed rational curves, we construct a K\\\"ahler potential in terms of the Fourier coefficients of the Klein's Hauptmodul. We define the space $\\mathfrak{S}_{g,n}$ as holomorphic fibration $\\mathfrak{S}_{g,n}\\rightarrow\\mathfrak{S}_{g}$ over the Schottky space $\\mathfrak{S}_{g}$ of compact Riemann surfaces of genus $g$, where the fibers are configuration spaces of $n$ points. For the tautological line bundles $\\mathscr{L}_{i}$ over $\\mathfrak{S}_{g,n}$ we define Hermitian metrics $h_{i}$ in terms of Fourier coefficients of a cove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02102","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":""},"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"}