Slicing Associated to a Plurisubharmonic Function

Abstract

In this paper, we study the slicing of currents, with respect to a locally bounded plurisubharmonic function. For a positive closed current and its associated Lelong-Skoda potential, we prove that, with respect to a smooth and strictly plurisubharmonic function, the slices are well defined except at points lying in a pluriplolar subset. In particular, the slices of the current of integration over an analytic set, are well defined explicitly, except at points lying in a countable family of proper analytic subsets. Furthermore, we state the analogue of the generalized slicing formula due to H. Ben Messaoud and H. El Mir.