#### Volume 21, issue 1 (2017)

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Shift operators and toric mirror theorem

### Hiroshi Iritani

Geometry & Topology 21 (2017) 315–343
##### 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 $I\phantom{\rule{0.3em}{0ex}}$–function and the mirror map. It also works for noncompact or nonsemipositive toric manifolds.

##### Keywords
mirror symmetry, Gromov–Witten invariants, quantum cohomology, torus action, toric variety, Givental cone, Seidel representation, shift operator
##### Mathematical Subject Classification 2010
Primary: 14N35, 53D45
Secondary: 14J33, 53D37