{"paper":{"title":"K\\\"ahler structure on Hurwitz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Georg Schumacher, Indranil Biswas, Reynir Axelsson","submitted_at":"2015-02-09T07:18:55Z","abstract_excerpt":"The classical Hurwitz spaces, that parameterize compact Riemann surfaces equipped with covering maps to ${\\mathbb P}_1$ of fixed numerical type with simple branch points, are extensively studied in the literature. We apply deformation theory, and present a study of the K\\\"ahler structure of the Hurwitz spaces, which reflects the variation of the complex structure of the Riemann surface as well as the variation of the meromorphic map. We introduce a generalized Weil-Petersson K\\\"ahler form on the Hurwitz space. This form turns out to be the curvature of a Quillen metric on a determinant line bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02384","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"}