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A note on planarity stratification of Hurwitz spaces

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

Abstract

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.

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