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