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Moduli stacks of sheaves on Calabi-Yau four-folds as critical loci

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Moduli stacks of sheaves on Calabi-Yau four-folds as critical loci
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The moduli stacks of sheaves on Calabi-Yau four-folds carry -2-shifted symplectic structures (Pantev, Toen, Vezzosi, Vaquie). Viewing these stacks as objects in differential geometry, one can construct Lagrangian foliations relative to these symplectic structures, such that quotients by the foliations are perfectly obstructed derived stacks, equipped with globally defined -1-shifted potentials, whose critical loci are the original moduli stacks. This is a joint work with A.Sheshmani and S-T.Yau.