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Local mirror symmetry of curves : Yukawa couplings and genus 1

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Title: Local mirror symmetry of curves : Yukawa couplings and genus 1
Authors: Forbes, Brian Browse this author
Jinzenji, Masao Browse this author →KAKEN DB
Issue Date: Jan-2007
Publisher: International Press
Journal Title: Advances in Theoretical and Mathematical Physics
Volume: 11
Issue: 1
Start Page: 175
End Page: 197
Abstract: 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.
Rights: ©2007 International Press
Type: article
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 秦泉寺 雅夫

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