ScalingStacks

Theorem 6.1 . [04Y6]

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Theorem 6.1.

Let XX be a maximally degenerate Calabi-Yau variety over KK of dimension nn, and assume that XX has a good dlt-model 𝒳\mathscr{X} over RR with reduced special fiber. Then the non-archimedean SYZ fibration

ρ𝒳:Xan→Sk⁡(X)\rho_{\mathscr{X}}\colon X^{\mathrm{an}}\to\mathrm{Sk}(X)

associated with 𝒳\mathscr{X} is an nn-dimensional affinoid torus fibration over the complement of some piecewise linear subset ZZ of Sk⁡(X)\mathrm{Sk}(X) of codimension ≥2\geq 2. Moreover, the induced integral affine structure on Sk⁡(X)∖Z\mathrm{Sk}(X)\setminus Z is compatible with the canonical piecewise integral affine structure on Sk⁡(X)\mathrm{Sk}(X) (see (2)), in the sense that they give rise to the same piecewise integral affine functions on Sk⁡(X)∖Z\mathrm{Sk}(X)\setminus Z.

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