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Local Mirror Symmetry: Calculations and Interpretations

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arxiv hep-th/9903053 v4 pith:ZXPGHHLU submitted 1999-03-05 hep-th math.AG

T.-M. Chiang , A. Klemm , S.-T. Yau , E. Zaslow This is my paper · ORCID
classification hep-thmath.AG
keywords localmirroragreecalculationsdescribegeometrypointsingular
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We describe local mirror symmetry from a mathematical point of view and make several A-model calculations using the mirror principle (localization). Our results agree with B-model computations from solutions of Picard-Fuchs differential equations constructed form the local geometry near a Fano surface within a Calabi-Yau manifold. We interpret the Gromov-Witten-type numbers from an enumerative point of view. We also describe the geometry of singular surfaces and show how the local invariants of singular surfaces agree with the smooth cases when they occur as complete intersections.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. BPS Invariants for Generalized Toric Calabi-Yau Threefolds

    hep-th 2026-07 conditional novelty 6.0 of 10

    Gopakumar–Vafa invariants are transported across Hanany–Witten transitions after removing a universal parallel-brane sector, giving first-time high-degree invariants for local dP4.

  2. An Airy Tale at Large $N$

    hep-th 2025-02 conditional novelty 6.0 of 10

    The paper presents numerical and analytic evidence that the large-N sphere partition function of five classes of M2-brane SCFTs, with squashing and real masses, takes the form of an Airy function to all orders in 1/N.

  3. BPS Dendroscopy on Local $\mathbb{P}^1\times \mathbb{P}^1$

    hep-th 2024-12 unverdicted novelty 6.0 of 10

    Construction of the scattering diagram for BPS indices on local P1 x P1 and sketch of the Split Attractor Flow Tree Conjecture for restricted central charge phase.

  4. Modular resurgence of topological string

    hep-th 2026-07 unverdicted novelty 5.0 of 10

    Stokes constants of topological string non-perturbative contributions are invariant on monodromy orbits, reproduce the BPS spectrum, and satisfy the Kontsevich-Soibelman Lie algebra.

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