The SYZ mirror identification conjecture for an anticanonical divisor

Let MM be the complexified moduli space of special Lagrangian tori in XDX\setminus D, let δ\delta be the class of the small holomorphic discs bounded by the circle fibers near the boundary, and let zδz_\delta be its associated coordinate. Define

MD={zδ=1}M.M_D=\{z_\delta=1\}\subset\partial M.

The SYZ mirror identification conjecture. The subset MDM_D is the Strominger–Yau–Zaslow mirror of DD. This identifies the mirror of the anticanonical divisor with the locus where the circle-fiber holonomy is trivial; the paper derives this from the proposed boundary behavior, but a general proof remains open.

Sources & referencesView supporting material

Primary source

Denis Auroux, “Mirror symmetry and T-duality in the complement of an anticanonical divisor”, arXiv:0706.3207 (2007).

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