New paper: Brauer groups of resolved quiver moduli via gerbes

I'm happy to announce a new paper, Brauer groups of resolved quiver moduli via gerbes, joint with Gianni Petrella and Sebastian Torres. In this paper we give a new and very different proof of an old result due to Le Bruyn and Schofield (two mathematicians I admire greatly!), by translating a proof (due to Biswas–Hogadi–Holla) in the context of moduli of vector bundles on curves to that of quiver moduli. It is no secret that the quiver-curve dictionary is a favourite topic of mine, and this paper can be seen as a contribution to this dictionary. The result in question says that the Brauer group of a resolution of any moduli space of quiver representations vanishes. If you believe that all quiver moduli (and moduli of vector bundles) are rational, then certainly this Brauer group has to vanish. Along the way of (re)proving this vanishing, we explain some interesting properties of quiver moduli, highlighting parallels (and differences) between the curve and quiver case. This project was…