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A Generalized Construction of Mirror Manifolds

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arxiv hep-th/9201014 v1 pith:2UJHYC42 submitted 1992-01-09 hep-th

P. Berglund , T. Hübsch This is my paper · ORCID
classification hep-th
keywords mirrorconstructionknownmanifoldstheoriescalabi-yauconstructexplicit
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abstract

We generalize the known method for explicit construction of mirror pairs of $(2,2)$-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known.

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Cited by 6 Pith papers

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

  1. The complete massless singlet spectrum in the free-field construction of heterotic strings on Calabi--Yau orbifolds

    hep-th 2026-07 conditional novelty 6.0 of 10

    The massless E6 singlet spectra of Fermat-type Calabi–Yau orbifolds are determined by Shapovalov ranks, yielding 330 singlets for the quintic and new counts 210 and 258 for two orbifolds.

  2. Beyond Algebraic Superstring Compactification

    hep-th 2025-02 conditional novelty 5.0 of 10

    Calabi-Yau compactifications and mirror symmetry are conjecturally extended to non-algebraic toric spaces using Laurent deformations and the 'intrinsic limit' completion.

  3. Ricci-Flat Mirror Hypersurfaces in Spaces of General Type

    hep-th 2025-01 conditional novelty 5.0 of 10

    Laurent-polynomial anticanonical sections can smooth Calabi-Yau hypersurfaces in general-type toric/torus manifolds and yield transposition mirrors with computable GLSM data.

  4. Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces

    hep-th 2024-03 unverdicted novelty 5.0 of 10

    Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.

  5. Free-Field Construction of Heterotic String Compactified on Calabi-Yau Orbifolds via Correspondence with $\mathcal{N}{=}2$ SCFT Minimal Models

    hep-th 2026-06 unverdicted novelty 4.0 of 10

    Correspondence between free-field and minimal-model constructions for the Calabi-Yau sector of heterotic strings on Berglund-Hübsch orbifolds, with modular invariance verification.

  6. Beyond Algebraic Solutions to Stringy Spacetime

    hep-th 2026-05 unverdicted novelty 3.0 of 10

    Generalizations beyond algebraic geometry in string theory remain aligned with mirror symmetry, support quantitative analysis, and point to deeper symplectic geometry connections.

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