{"paper":{"title":"Estimates of Bergman Kernels and Bergman metric on compact Picard surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anilatmaja Aryasomayajula, Debasish Sadhukhan, Dyuti Roy","submitted_at":"2023-12-19T03:30:39Z","abstract_excerpt":"Let $\\Gamma\\subset \\mathrm{SU}((2,1),\\mathbb{C})$ be a torsion-free cocompact subgroup. Let $\\mathbb{B}^{2}$ denote the $2$-dimensional complex ball endowed with the hyperbolic metric $\\mu_{\\mathrm{hyp}}$, and let $X_{\\Gamma}:=\\Gamma\\backslash \\mathbb{B}^{2}$ denote the quotient space, which is a compact complex manifold of dimension $2$. Let $\\Lambda:= \\Omega_{X_{\\Gamma}}^{2}$ denote the line bundle on $X_{\\Gamma}$, whose sections are holomorphic $(2,0)$-forms. For any $k\\geq 1$, the hyperbolic metric induces a point-wise metric on $H^{0}(X_{\\Gamma},\\Lambda^{\\otimes k })$, which we denote by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11824","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.11824/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"}