Kähler geometry on Hurwitz spaces

2016/12/07 by Philipp Naumann, Naumann, Philipp
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1612.02197

openalex publication_date 2016/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Kähler geometry of the classical Hurwitz space H^n,b of simple branched coverings of the Riemann sphere ℙ¹ by compact hyperbolic Riemann surfaces. A generalized Weil-Petersson metric on the Hurwitz space was recently introduced. Deformations of simple branched coverings fit into the more general framework of Horikawa's deformation theory of holomorphic maps, which we equip with distinguished representatives in the presence of hermitian metrics. In the article we will investigate the curvature of the generalized Weil-Petersson Kähler metric on the Hurwitz space.

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