{"paper":{"title":"Estimates of K\\\"ahler metrics on noncompact finite volume hyperbolic Riemann surfaces, and their symmetric products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Anilatmaja Aryasomayajula, Arijit Mukherjee","submitted_at":"2023-05-19T11:38:47Z","abstract_excerpt":"Let $X$ denote a noncompact finite volume hyperbolic Riemann surface of genus $g\\geq 2$, with only one puncture at $i\\infty$ (identifying $X$ with its universal cover $\\mathbb{H}$). Let $\\overline{X}:=X\\cup\\lbrace i\\infty\\rbrace$ denote the Satake compactification of $X$. Let $\\Omega_{\\overline{X}}$ denote the cotangent bundle on $\\overline{X}$. For $k\\gg1$, we derive an estimate for $\\mu_{\\overline{X}}^{\\mathrm{Ber},k}$, the Bergman metric associated to the line bundle $\\mathcal{L}^{k}:=\\Omega_{\\overline{X}}\\otimes \\mathcal{O}_{\\overline{X}}\\big((k-1)\\infty\\big)$.\n  For a given $d\\geq 1$, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.11609","kind":"arxiv","version":3},"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/2305.11609/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"}