
TL;DR
This paper connects counts of normalized real polynomials to counts of genus zero real ramified coverings of the Riemann sphere, providing a new perspective on real Hurwitz numbers.
Contribution
It establishes a correspondence between signed counts of normalized real polynomials and genus zero real ramified coverings with specific ramification profiles.
Findings
Counts of normalized real polynomials match counts of certain real ramified coverings.
Provides a new interpretation of real Hurwitz numbers in terms of polynomial counts.
Extends previous work by Itenberg and Zvonkine on signed polynomial counts.
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Holomorphic and Operator Theory · Geometry and complex manifolds
