English

Relative critical loci and quiver moduli

Representation Theory 2024-04-04 v4 Algebraic Geometry Algebraic Topology Category Theory Symplectic Geometry

Abstract

In this paper we identify the cotangent to the derived stack of representations of a quiver QQ with the derived moduli stack of modules over the Ginzburg dg-algebra associated with QQ. 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.

Keywords

Cite

@article{arxiv.2006.01069,
  title  = {Relative critical loci and quiver moduli},
  author = {Tristan Bozec and Damien Calaque and Sarah Scherotzke},
  journal= {arXiv preprint arXiv:2006.01069},
  year   = {2024}
}

Comments

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

R2 v1 2026-06-23T15:58:04.100Z