ScalingStacks

Definition 3.1 [03KX]

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Definition 3.1 Let (X,J,ω,Ω)(X,J,\omega,\Omega) be a Calabi–Yau or almost Calabi–Yau 3-fold, and f:X→Bf:X\rightarrow B a special Lagrangian fibration of (X,J,ω,Ω)(X,J,\omega,\Omega). We shall say that some property of ff is generic if for all Kähler forms ω~\tilde{\omega} on XX in the same Kähler class as ω\omega and sufficiently close to ω\omega, there exists close to ff a special Lagrangian fibration f~:X→B\tilde{f}:X\rightarrow B of the almost Calabi–Yau 3-fold (X,J,ω~,Ω)(X,J,\tilde{\omega},\Omega) with the same property. Examples of properties of ff that might or might not be generic are: existence, smoothness, every singular fibre has only finitely many singular points, and so on.

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