On Frobenius Manifolds from Gromov--Witten Theory of Orbifold Projective Lines with $r$ orbifold points

TL;DR

This paper proves that the Frobenius structure derived from Gromov-Witten theory for orbifold projective lines with up to r orbifold points is uniquely determined by the WDVV equations and natural initial conditions.

Contribution

It establishes the uniqueness of the Frobenius structure from Gromov-Witten theory for orbifold projective lines with specified orbifold points.

Findings

Uniqueness of Frobenius structure proven

Determination by WDVV equations and initial conditions

Applicable to orbifold projective lines with up to r orbifold points

Abstract

We prove that the Frobenius structure constructed from the Gromov-Witten theory for an orbifold projective line with at most $r$ orbifold points is uniquely determined by the WDVV equations with certain natural initial conditions.