open access

https://hdl.handle.net/2115/30115

Local mirror symmetry of curves : Yukawa couplings and genus 1

英語

2007-01

International Press

Advances in Theoretical and Mathematical Physics

11(1)

175-197

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.

学術雑誌論文

Version of Record

©2007 International Press

1095-0761

1095-0753