ScalingStacks

Theorem 1.1 . [00PH]

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Theorem 1.1.

(cf. section 5.4) For the Fermat family, consider the Calabi-Yau metrics on XsX_{s} in the polarisation class s−1​[Δ]s^{-1}[\Delta] where [Δ][\Delta] is a fixed Kähler class on ℂ​ℙn+1\mathbb{CP}^{n+1} restricted to XsX_{s}. Then for a subsequence of XsX_{s} as s→+∞s\to+\infty, there exists a special Lagrangian TnT^{n}-fibration on the generic region Us⊂XsU_{s}\subset X_{s}, such that Vol​(Us)Vol​(Xs)→1\frac{\text{Vol}(U_{s})}{\text{Vol}(X_{s})}\to 1 as s→+∞s\to+\infty.

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