A Uniqueness Theorem for Frobenius Manifolds and Gromov--Witten Theory for Orbifold Projective Lines

TL;DR

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

Contribution

It establishes a uniqueness theorem linking Frobenius structures to Gromov-Witten invariants for orbifold projective lines.

Findings

Uniqueness of Frobenius structures for orbifold projective lines with up to three orbifold points.

Connection between WDVV equations and Gromov-Witten invariants.

Clarification of initial conditions determining the Frobenius structure.

Abstract

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