Speaker
Description
In this talk, we consider the quotient singularities associated to some
special linear actions of finite groups without pseudo-reflections. In
characteristic $0$, the age grading on the group, which relies on the
existence of the primitive roots of unity, is useful to study the properties
of the quotient singularities. On the other hand, when the characteristic
$p$ is positive, the age grading cannot be defined on the $p$-subgroups.
Instead, the invariant $D_V$ was introduced by Yasuda to study the linear
$p$-cyclic quotients. After a historical overview to the invariant $D_V$,
we will illustrate its role through recent developments, including the
criterion for cyclic quotients to be terminal or canonical, the construction
of crepant models, and the predicting formulas for the Euler
characteristics of crepant resolutions. This talk is based in part on
joint work with Hongmin Li.