Shift operators and toric mirror theorem

Iritani, Hiroshi¹

¹ Department of Mathematics, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan

Geometry & topology, Tome 21 (2017) no. 1, pp. 315-343.

Résumé

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.

Détail

DOI : 10.2140/gt.2017.21.315

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

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