On piecewise pluriharmonic functions
  We extend some results on piecewise linear functions on $\C^n$ to piecewise pluriharmonic functions on any complex manifold.   We construct a ring generated by currents $h$ and $dd^ch$, where $\{h\}$ is a finite set of piecewise pluriharmonic functions.   We prove that, with some restrictions on the set $\{h\}$, the map $\{h\mapsto dd^ch,\ dd^ch\mapsto0\}$ can be continued to the derivation on the ring.   As a corollary, the current $dd^cg_1\wedge...\wedge dd^cg_k$ depends on the product of piecewise pluriharmonic functions $g_1,...,g_k$ only. 
Boris Kazarnovskii
math.CV