DIRECT IMAGES OF SEMI-MEROMORPHIC CURRENTS

We introduce a calculus for the class ASM(X) of direct images of semi-meromorphic currents on a reduded analytic space X, that extends the classical calculus due to Coleff, Herrera and Passare. Our main result is that each element in this class acts as a kind of multiplication on the sheaf PMX of pseudomeromorphic currents on X. We also prove that ASM(X) as well as PMX and certain subsheaves are closed under the action of holomorphic differential operators and interior multiplication by holomorphic vector fields.