Relative critical loci and quiver moduli

Tristan Bozec (1) , Damien Calaque (1) , Sarah Scherotzke (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Uni.lu - Université du Luxembourg

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.

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]; Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]; Géométrie symplectique [math.SG]

Tristan Bozec, Damien Calaque, Sarah Scherotzke. Relative critical loci and quiver moduli. 2024. ⟨hal-02861404⟩