KASS seminar

Abstract: In the study of plurisubharmonic singularities on projective manifolds, it is important to make induction on the dimension of the underlying manifold. It is therefore desirable to have a well-behaved restriction operator of closed positive (1,1)-currents T from a manifold X to a divisor D. When D is in general position, the analytic Bertini theorem shows that the naive restriction is well-behaved. While for special D, the naive restriction may fail to give useful information. As an example, when T has log-log singularities along D, the naive restriction of T to D even fails to exist. However, log-log singularities are almost as good as non-singular currents. I will explain how to define a correct restriction (the trace operator) in this case. This talk is based on a joint work with T. Darvas (https://arxiv.org/abs/2403.08259).