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

TL;DR

This paper constructs globally defined Lagrangian distributions on derived Quot-stacks of sheaves on Calabi-Yau four-folds, leading to smooth stacks with globally defined shifted potentials that recover the stable loci in a Darboux form.

Contribution

It introduces a method to produce globally defined shifted potentials on moduli stacks of sheaves on Calabi-Yau four-folds, enhancing the understanding of their geometric and derived structures.

Findings

Existence of globally defined Lagrangian distributions on stable loci

Construction of perfectly obstructed smooth stacks with shifted potentials

Recovery of stable loci as derived critical loci in Darboux form

Abstract

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.