Real polynomial Hurwitz numbers

2025/06/20 by Ding, Yanqiao
#14H30 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Primary 14N10 #Secondary 14P05

paper · doi:10.48550/arxiv.2506.16879

Abstract

We show that the signed counts of normalized real polynomials, as defined by Itenberg and Zvonkine, provide the signed counts of genus zero real ramified coverings of the Riemann sphere with a point of total ramification and several other branch points with arbitrary ramification profiles.

Citations

• The uniform asymptotics for real double Hurwitz numbers with triple ramification I: the tropical correspondence
• Asymptotics for real monotone double Hurwitz numbers
• Tropical Open Hurwitz numbers
• Enumerative tropical algebraic geometry in R2
• Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants
• Towards the geometry of double Hurwitz numbers
• Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry

Related

• The structure of Hurwitz numbers with fixed ramification profile and varying genus
• Bijections for simple and double Hurwitz numbers
• Real algebraic curves and twisted Hurwitz numbers
• The uniform asymptotics for real double Hurwitz numbers with triple ramification I: the tropical correspondence
• On \mathbb N-Coefficient Binomial Polynomiality of Hurwitz Numbers and Generalized Dessin Counting