We continue our study of equivariant local mirror symmetry of curves, i.e., mirror symmetry for Xk - O(k) ⊕ O(-2 - k) → ℙ1 with torus action (λ1,λ2) on the bundle. For the antidiagonal action λ1 = - λ2, we find closed formulas for the mirror map, a rational B model Yukawa coupling and consequently Picard-Fuchs equations for all k. Moreover, we give a simple closed form for the B model genus 1 Gromov-Witten potential. For the diagonal action λ1 = λ2, we argue that the mirror symmetry computation is equivalent to that of the projective bundle ℙ(O ⊕ O(k) ⊕O(-2 - k)) → ℙ1. Finally, we outline the computation of equivariant Gromov-Witten invariants for An singularities and toric tree examples via mirror symmetry.
ASJC Scopus subject areas
- Physics and Astronomy(all)