{"paper":{"title":"Complex hyperbolic volume and intersection of boundary divisors in moduli spaces of genus zero curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Duc-Manh Nguyen, Vincent Koziarz","submitted_at":"2016-01-20T12:26:28Z","abstract_excerpt":"We show that the complex hyperbolic metrics defined by Deligne-Mostow and Thurston on ${\\mathcal{M}}_{0,n}$ are singular K\\\"ahler-Einstein metrics when ${\\mathcal{M}}_{0,n}$ is embedded in the Deligne-Mumford-Knudsen compactification $\\overline{\\mathcal{M}}_{0,n}$. As a consequence, we obtain a formula computing the volumes of ${\\mathcal{M}}_{0,n}$ with respect to these metrics using intersection of boundary divisors of $\\overline{\\mathcal{M}}_{0,n}$. In the case of rational weights, following an idea of Y. Kawamata, we show that these metrics actually represent the first Chern class of some l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05252","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"}