Tropical Jucys Covers

TL;DR

This paper explores the connections between monotone Hurwitz numbers, tropical geometry, and Gromov-Witten invariants, revealing refinements in the Gromov-Witten/Hurwitz correspondence through a bosonic Fock space approach.

Contribution

It introduces a novel interpretation of monotone Hurwitz numbers in tropical geometry and refines the Gromov-Witten/Hurwitz correspondence using this framework.

Findings

Tropical interpretation of monotone Hurwitz numbers

Refinement of Gromov-Witten/Hurwitz correspondence

Bosonic Fock space approach to enumerative geometry

Abstract

We study monotone and strictly monotone Hurwitz numbers from a bosonic Fock space perspective. This yields to an interpretation in terms of tropical geometry involving local multiplicities given by Gromov-Witten invariants. Furthermore, this enables us to prove that a main result of Cavalieri-Johnson-Markwig-Ranganathan is a actually a refinement of the Gromov-Witten/Hurwitz correspondence by Okounkov-Pandharipande.