Counting curves on orbifolds

TL;DR

This paper extends Mirzakhani's curve counting theorem from surfaces to orbifolds, demonstrating that the counting principles apply in this broader geometric context.

Contribution

It introduces a generalization of Mirzakhani's theorem, adapting the curve counting framework to orbifolds.

Findings

Curve counting formulas valid for orbifolds

Extension of Mirzakhani's theorem to new geometric settings

Broader applicability of curve counting techniques

Abstract

We show that Mirzakhani's curve counting theorem also holds if we replace surfaces by orbifolds.