Projectivity of good moduli spaces of quiver representations

Vortrag von Dr. Tuomas Tajakka

Sprecher eingeladen von: Prof. Dr. Joseph Ayoub

Datum: 07.06.22  Zeit: 13.15 - 14.45  Raum: Y27H12

Quiver representations and their moduli spaces are central objects of study in algebraic geometry and representation theory. In 1994, King constructed these moduli spaces as projective varieties using GIT. The goal of this talk is to give a new construction avoiding GIT, instead utilizing the machinery of algebraic stacks and their good moduli spaces. Using results of Alper--Halpern-Leistner--Heinloth, we show that the moduli stack of semistable quiver representations admits a proper good moduli space, on which we exhibit an ample determinantal line bundle. We also obtain effective bounds for global generation of this bundle. Joint work with Pieter Belmans, Chiara Damiolini, Hans Franzen, Victoria Hoskins, and Svetlana Makarova.