Prolongement méromorphe des courants de Green. (Meromorphic continuation of Green currents.) (Q697379)

Let \(X\) be a quasi-projective smooth complex variety, let \(Y\), \(Z\subset X\) be subvarieties with proper intersection, and let \(g_Y\), \(g_Z\) be Green currents on \(Y\) and \(Z\), respectively (a current \(g_Y\) of type \((p-1,p-1)\) (\(p:=\text{codim}Y\)) is a Green current if \(dd^cg_Y+\delta_Y=\omega\) for a form \(\omega\), where \(\delta_Y\) is the integration current of \(Y\)). The author presents a new approach to the definition of the \(\ast\)-product \(g_Y\ast g_Z:=g_Y\cdot\delta_Z+\delta_Y\cdot g_Z\) based on meromorphic continuation of currents.