Equivariant mirror symmetry for the weighted projective line

TL;DR

This paper proves equivariant mirror symmetry for the weighted projective line by demonstrating the equivalence of R-matrices in A-model and B-model across different radii, extending prior results for the projective line.

Contribution

It extends equivariant mirror symmetry results from the projective line to the weighted projective line, including R-matrix equivalences and higher genus graph sum comparisons.

Findings

R-matrices for A-model and B-model are equivalent at large radius

Isomorphism of R-matrices established for general radius

Higher genus graph sums are identical for both models

Abstract

In this paper, we establish equivariant mirror symmetry for the weighted projective line. This extends the results by B. Fang, C.C. Liu and Z. Zong, where the projective line was considered [{\it Geometry \& Topology} 24:2049-2092, 2017]. More precisely, we prove the equivalence of the $R$-matrices for A-model and B-model at large radius limit, and establish isomorphism for $R$-matrices for general radius. We further demonstrate that the graph sum of higher genus cases are the same for both models, hence establish equivariant mirror symmetry for the weighted projective line.