Research demonstrates the existence of Lagrangian distributions in stacks of sheaves on Calabi-Yau four-folds, highlighting new structures.
It is shown that there are globally defined Lagrangian distributions on the stable loci of derived Quot-stacks of coherent sheaves on Calabi--Yau four-folds. Dividing by these distributions produces perfectly obstructed smooth stacks with globally defined $-1$-shifted potentials, whose derived critical loci give back the stable loci of smooth stacks of sheaves in global Darboux form.
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Borisov et al. (2026) studied this question.
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