In this talk, we will discuss the minimal log discrepancies of quotient singularities. I will show that the PIA (precise inversion of adjunction) conjecture holds for quotient singularities. The main tool of this talk involves the theory of the arc space of a quotient singularity established by Denef and Loeser. I will also explain some technical difficulties when dealing with non-linear group actions.
This is joint work with Kohsuke Shibata.
This video was produced by the Japan-US Mathematics Institute and forms part of JAMI Conference 2022.
