A Non-Abelian Approach to Riemann Surfaces Part I: Wronskian Geometry

2025/11/15 by Mehrzad Ajoodanian, Ajoodanian, Mehrzad
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2511.12337

openalex publication_date 2025/11/15 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28

Abstract

We study projectively flat holomorphic vector bundles over Riemann surfaces. To each such bundle, we naturally assign a Wronskian line bundle. The main idea is a notion of the division of two meromorphic sections. Abel's identity is interpreted as the first Chern class of the Wronskian line bundle.

Citations

• On Abel's Identity

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