Shift operators and toric mirror theorem

Abstract

We give a new proof of Givental's mirror theorem for toric manifolds using shift operators of equivariant parameters. The proof is almost tautological: it gives an A-model construction of the I-function and the mirror map. It also works for non-compact or non-semipositive toric manifolds.

24 pages, v2: I corrected a mistake in the differential equation for Upsilon; proof simplified a little

References in corpus (2)

• A Mirror Theorem for Toric Stacks
• A mirror construction for the big equivariant quantum cohomology of toric manifolds

Cited by in corpus (2)

• Quantum Steenrod operations of symplectic resolutions
• Equivariant Homological Mirror Symmetry for $\mathbb{C}$ and $\mathbb{C}{P}^1$