Real algebraic curves and twisted Hurwitz numbers

2024/03/10 by Yurii Burman, Burman, Yurii, Raphaël Fesler +1
Computer Science · Mathematics · #05A05 #05A19 #57M12 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2403.06171

openalex publication_date 2024/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a direct correspondence between the b-Hurwitz numbers with b=1 from \citeChapuyDolega, and twisted Hurwtiz numbers from \citeTwistedHurwitz. This provides a description of real coverings of the sphere with ramification on the real line in terms of monodromy.

Related

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• Bijections for simple and double Hurwitz numbers
• Recursions, formulas, and graph-theoretic interpretations of ramified coverings of the sphere by surfaces of genus 0 and 1
• Real polynomial Hurwitz numbers
• Towards the topological recursion for double Hurwitz numbers