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Mirror Symmetry and the Strominger-Yau-Zaslow conjecture

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arxiv 1212.4220 v2 pith:GW7AWUV3 submitted 2012-12-18 math.AG math.DGmath.SG

Mark Gross This is my paper · ORCID
classification math.AGmath.DGmath.SG
keywords conjectureexplainprogramstrominger-yau-zaslowalgebro-geometricarticlebeginconference
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This survey was written for the Current Developments in Mathematics conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations," in the Seattle 2005 proceedings. We trace progress and thinking about the SYZ conjecture since its introduction in 1996. We begin with the original differential geometric conjecture and its refinements, and explain how it led to the algebro-geometric program developed by myself and Siebert. After explaining the overall philosophy, I explain how recent results fit into this program.

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Cited by 2 Pith papers

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

  1. Almost toric fibrations on K3 surfaces via degenerations

    math.SG 2025-02 conditional novelty 7.0 of 10

    Symplectic Kulikov models of K3 surfaces yield almost toric fibrations on the smooth fiber, with the Gross-Siebert affine structure for anticanonical hypersurfaces in toric Fano threefolds.

  2. Special Lagrangian submanifolds and circle collapse on K3

    math.DG 2026-06 unverdicted novelty 5.0 of 10

    Constructs degenerating special Lagrangian two-spheres and tori in collapsing K3 surfaces that lift from affine lines on a three-dimensional base, including connections between Taub-NUT bubbles.

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