  We analyse a system of arbitrarily intersecting D-branes in ten-dimensional
supergravity. Chiral anomalies are supported on the intersection branes, called
I-branes. For non-transversal intersections anomaly cancellation has been
realized until now only cohomologically but not locally, due to short-distance
singularities. In this paper we present a consistent local cancellation
mechanism, writing the delta-like brane currents as differentials of the
recently introduced Chern--kernels, J=dK. In particular, for the first time we
achieve anomaly cancellation for dual pairs of D-branes. The Chern-kernel
approach allows to construct an effective action for the RR-fields which is
free from singularities and cancels the quantum anomalies on all D-branes and
I-branes.
