Tropical Open Hurwitz numbers
Benoit Bertrand, Erwan Brugalle, Grigory Mikhalkin
TL;DR
This paper introduces a tropical geometric interpretation of Hurwitz numbers, including a new generalization called open Hurwitz numbers for surfaces with boundary, expanding the understanding of these enumerative invariants.
Contribution
It extends the tropical approach to Hurwitz numbers and introduces open Hurwitz numbers for bordered surfaces, broadening the scope of tropical enumerative geometry.
Findings
Tropical interpretation of classical Hurwitz numbers.
Definition of open Hurwitz numbers for surfaces with boundary.
Extension of tropical methods to new classes of enumerative problems.
Abstract
We give a tropical interpretation of Hurwitz numbers extending the one discovered in \cite{CJM}. In addition we treat a generalization of Hurwitz numbers for surfaces with boundary which we call open Hurwitz numbers.
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