Pluri-polarity in almost complex structures (Q966450)

A new proof of the pluripolarity of \(J\)-holomorphic curves is established. The non existence of functions with logarithmic singularity is shown under natural reasonable hypotheses on the behaviour of the function and then the non existence result is proved in full generality. In this context, an example in dimension \(4\) is given showing that, in general, \(J\)-holomorphic curves are not \(-\infty\) set of any \(J\)-plurisubharmonic function with a logarithmic singularity. The case when the Nijenhuis tensor of the almost complex structure \(J\) vanishes along a \(J\)-holomorphic disc is treated, where functions with logarithmic poles exist. Finally, some important remarks in dimension \(4\) and in higher dimension \(2n\) are discussed.