Relative critical loci, quiver moduli, and new lagrangian subvarieties



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PIRSA Number: 
20060045

Abstract

The preprojective algebra of a quiver naturally appears when computing
the cotangent to the quiver moduli, via the moment map. When considering
the derived setting, it is replaced by its differential graded (dg)
variant, introduced by Ginzburg. This construction can be generalized
using potentials, so that one retrieves critical loci when considering
moduli of perfect modules.
Our idea is to consider some relative, or constrained critical loci,
deformations of the above, and study Calabi--Yau structures on the
underlying relative versions of Ginzburg's dg-algebras. It yields for
instance some new lagrangian subvarieties of the Hilbert schemes of
points on the plane.

This reports a joint work with Damien Calaque and Sarah Scherotzke
arxiv.org/abs/2006.01069