Reinier Schmiermann (Utrecht) - Counting modules over a noncommutative resolution of C^4/(Z/2)

Consider the singularity C^4/(Z/2), where Z/2 acts as the matrix diag(-1,-1,-1,-1). This singularity is special, in that it does not admit a crepant resolution. However, it does admit a so-called noncommutative crepant resolution, given by a Calabi-Yau 4 quiver. The moduli space of representations of this quiver turns out to share a lot of similarities with moduli spaces of sheaves over Calabi-Yau fourfolds, and it turns out that we can reuse techniques from studying moduli of sheaves to define and compute invariants of this moduli space of representations. In this talk, I will explain how these invariants can be defined, and give conjectures about the forms of these invariants. This talk is based on joint work with Raf Bocklandt.

Published Sep. 14, 2022 10:35 AM - Last modified Dec. 5, 2022 2:32 PM