Seidel elements and mirror transformations

Abstract

The goal of this article is to give a precise relation between the mirror symmetry transformation of Givental and the Seidel elements for a smooth projective toric variety $X$ with $-K_X$ nef. We show that the Seidel elements entirely determine the mirror transformation and mirror coordinates.

36 pages. We corrected several issues as pointed out by the referee

Cited by in corpus (6)

• Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
• Enumerative meaning of mirror maps for toric Calabi-Yau manifolds
• Shift operators and toric mirror theorem
• Seidel elements and potential functions of holomorphic disc counting
• A Note on Disk Counting in Toric Orbifolds
• Non-contractible Hamiltonian loops in the kernel of Seidel's representation