2014/08/28 by J. Ongaro, B. Shapiro, Ongaro, J. +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.AG
paper · pdf · doi:10.48550/arxiv.1408.6797
12 pages
arxiv created 2014/08/28 · openalex publication_date 2014/08/28 · arxiv updated 2014/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One can easily show that any meromorphic function on a complex closed Riemann surface can be represented as a composition of a birational map of this surface to CP2 and a projection of the image curve from an appropriate point p in CP2 to the pencil of lines through p. We introduce a natural stratification of Hurwitz spaces according to the minimal degree of a plane curve such that a given meromorphic function can be represented in the above way and calculate the dimensions of these strata.