Computing Green Currents via the Heat Kernel

Abstract

Let X be a compact Kähler manifold. We show that there exists a unique Green current gY for any cycle Y in X. We show that the current gY is a form with L1-coefficients. The heat kernel applied to the Dirac distribution associated with Y plays a central role in this construction. Furthermore, we show how these Green currents fit into intersection theory. Finally, we compute this canonical current for some examples.