Problem 3.12 . [03P1]
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Problem 3.12.
(a) Choose from the literature your favourite family of explicit, nonsingular, exact SL -folds in which converge to an explicit singular SL -fold as . For example, let be an exact AC SL -fold in with cone and take for and .
Construct examples of Lagrangian MCF in or in a Calabi–Yau -fold with finite time singularities at for which has a singularity at modelled on and near for approximates where as as in Principle 3.9(a).
(b) If you can do (a), determine whether Lagrangian MCF starting from a small generic Hamiltonian perturbation of also develops finite time singularities of the same type. In this case, we call this type a generic singularity of Lagrangian MCF. If it is not generic, compute the expected codimension amongst Hamiltonian perturbations of in which singularities of this type occur.
(c) Repeat (a),(b) for LMCF translators rather than SL -folds.