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Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties

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arxiv alg-geom/9310001 v1 pith:CRYDPFHX submitted 1993-10-02 alg-geom math.AG

Lev Borisov This is my paper · ORCID
classification alg-geommath.AG
keywords calabi-yaucompletedualityfanogorensteinintersectionsmirrortoric
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We propose a combinatorical duality for lattice polyhedra which conjecturally gives rise to the pairs of mirror symmetric families of Calabi-Yau complete intersections in toric Fano varieties with Gorenstein singularities. Our construction is a generalization of the polar duality proposed by Batyrev for the case of hypersurfaces.

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Forward citations

Cited by 5 Pith papers

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

  1. Lagrangian skeleta of very affine complete intersections

    math.SG 2025-10 conditional novelty 8.0 of 10

    The Lagrangian skeleton of an open Batyrev–Borisov complete intersection is a sphere-with-tori inside an FLTZ skeleton, yielding homological mirror symmetry at the large-volume limit.

  2. Abelian Orbifolds for Brane Brick Models

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    A construction procedure that induces an abelian orbifold action on the fields and J/E-terms of a parent brane brick model for a toric CY4, yielding explicit orbifolded theories that preserve consistency conditions.

  3. Non-commutative resolutions and pre-quotients of Calabi-Yau double covers

    hep-th 2025-07 conditional novelty 7.0 of 10

    A-periods of non-commutative resolutions of Calabi-Yau double covers satisfy the same GKZ system as those of an explicitly constructed smooth complete intersection.

  4. Calabi-Yau Orientifold Hypersurfaces and their F-theory Uplifts

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    An algorithm builds Calabi-Yau orientifolds and F-theory fourfold uplifts from 6d reflexive polytopes derived from orientifold data, with code in CYTools and GitHub.

  5. Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds

    hep-th 2025-02 conditional novelty 5.0 of 10

    Mass deformations of 2d (0,2) brane brick models are shown in four explicit examples to implement birational transformations of toric Calabi-Yau 4-folds, including non-reflexive toric diagrams.

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