Oka's inequality for currents and applications
A version of Oka's inequality for currents of the form \(uT\) is given, where \(T\) is a positive closed current of bidimension \((p,p)\) and \(u\) is a negative plurisubharmonic function. It follows that the set where \(uT\) has a locally bounded mass is \(p\)-pseudoconvex (using a convention where \((n - 1)\)-pseudoconvexity is the usual pseudoconvexity). When \(uT\) has a locally bounded mass a convergence result is proved for the operator \[ (u_1 \ldots u_p) \to dd^cu_1 \wedge \cdots \wedge dd^c u_p \wedge T. \] This leads to a Bezout type theorem in \(\mathbb{P}^k\) with an application to holomorphic dynamics in \(\mathbb{P}^k\).
scientific article; zbMATH DE number 759274
scientific article