## Abstract

We continue our study of equivariant local mirror symmetry of curves, i.e., mirror symmetry for X_{k} - O(k) ⊕ O(-2 - k) → ℙ^{1} with torus action (λ_{1},λ_{2}) on the bundle. For the antidiagonal action λ_{1} = - λ_{2}, 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 λ_{1} = λ_{2}, we argue that the mirror symmetry computation is equivalent to that of the projective bundle ℙ(O ⊕ O(k) ⊕O(-2 - k)) → ℙ^{1}. Finally, we outline the computation of equivariant Gromov-Witten invariants for A_{n} singularities and toric tree examples via mirror symmetry.

Original language | English |
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Pages (from-to) | 175-197 |

Number of pages | 23 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 11 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 |

Externally published | Yes |

## ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)