Relative critical loci and quiver moduli

Abstract

In this paper we identify the cotangent to the derived stack of representations of a quiver $Q$ with the derived moduli stack of modules over the Ginzburg dg-algebra associated with $Q$. More generally, we extend this result to finite type dg-categories, to a relative setting as well, and to deformations of these. It allows us to recover and generalize some results of Yeung, and leads us to the discovery of seemingly new lagrangian subvarieties in the Hilbert scheme of points in the plane.

arXiv comment59 pages. v4: only cosmetical changes. This is the final version to appear in Annales Scientifiques de l'ENS

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Cited by in corpus (5)

• Shifted symplectic reduction of derived critical loci
• Calabi-Yau structures for multiplicative preprojective algebras
• McKay correspondence, cohomological Hall algebras and categorification
• Singular Legendrian unknot links and relative Ginzburg algebras
• Derived equivalences of upper-triangular ring spectra via lax limits