Chiodo formulas for the r-th roots and topological recursion

TL;DR

This paper connects Chiodo's formulas for r-th root Chern classes with topological recursion, providing new proofs and insights into orbifold Hurwitz numbers and their enumerative geometry.

Contribution

It demonstrates that intersection numbers of Chiodo classes can be computed via topological recursion and proves the equivalence of the Johnson-Pandharipande-Tseng formula with topological recursion for orbifold Hurwitz numbers.

Findings

Intersection numbers are reproduced by topological recursion.

Johnson-Pandharipande-Tseng formula is equivalent to topological recursion.

Provides a new proof of topological recursion for orbifold Hurwitz numbers.

Abstract

We analyze Chiodo's formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with psi-classes are reproduced via the Chekhov-Eynard-Orantin topological recursion. As an application, we prove that the Johnson-Pandharipande-Tseng formula for the orbifold Hurwitz numbers is equivalent to the topological recursion for the orbifold Hurwitz numbers. In particular, this gives a new proof of the topological recursion for the orbifold Hurwitz numbers.