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Shift operators and toric mirror theorem

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arxiv 1411.6840 v2 pith:CNBYWOTG submitted 2014-11-25 math.AG math.SG

Hiroshi Iritani This is my paper · ORCID
classification math.AGmath.SG
keywords mirrortoricmanifoldsoperatorsproofshifttheorema-model
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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.

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  1. Fourier analysis of equivariant quantum cohomology

    math.AG 2025-01 conditional novelty 7.0 of 10

    Equivariant quantum cohomology and the quantum cohomology of a GIT quotient are conjectured to be Fourier duals, with the quotient's I-function expressed as a discrete Fourier transform of the equivariant J-function.

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