Global shifted potentials for moduli stacks of sheaves on Calabi-Yau four-folds

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 cri...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Borisov, Dennis, Katzarkov, Ludmil, Artan Sheshmani, Shing-Tung Yau
Format: Article
Language:English
Subjects:
Loci
Sheaves
Stacks
Online Access:Get full text
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Summary: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.
ISSN:2331-8422