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Shift operators and toric mirror theorem

Hiroshi Iritani
Geometry & Topology 21 (2017) 315–343
DOI: 10.2140/gt.2017.21.315
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 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
References
Publication
Received: 4 January 2015
Accepted: 26 February 2016
Published: 10 February 2017
Proposed: Jim Bryan
Seconded: Richard Thomas, Yasha Eliashberg
Authors
Hiroshi Iritani
Department of Mathematics, Graduate School of Science
Kyoto University
Kitashirakawa-Oiwake-cho
Sakyo-ku
Kyoto 606-8502
Japan