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 with the derived moduli stack of modules over the Ginzburg dg-algebra associated with . 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.
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