In the picture of the metric collapse for Calabi-Yau manifolds (Gross-Wilson and Kontsevich-Soibelman) I propose to use the generalized
Gibbons-Hawking ansatz to analize the local behavior of the metric near the discriminant locus of the SYZ torus fibration. After a change of coordinates (partial Legendre transform) the limiting PDE on the metric potential are
exactly the real Monge-Ampere equations with the monodromy encoded in the singularities of solutions.
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