On Newton Diagrams of Plurisubharmonic Polynomials

Abstract

Each extreme edge of the Newton diagram of a plurisubharmonic polynomial on C2 gives rise to a plurisubharmonic polynomial. It is tempting to believe that the union of the extreme edges or the convex hull of said union will do the same. If true, then the latter would provide useful strategies for the bumping of plurisubharmonic polynomials on C2 , but whether they are true has been elusive until now. We construct a plurisubharmonic polynomial P on C2 with precisely two extreme edges E1 and E2 , such that neither E1∪E2 nor Conv(E1∪E2) yields a plurisubharmonic polynomial.