Residual currents and fundamental class (Q1901187)

Let \(Y\) be the complex subspace of a complex manifold \(X\) defined by a coherent ideal \(I\), which is a locally complete intersection. The authors introduce the notion of the cohomology with supports in the infinitesimal neighbourhood of first order of \(Y\) and then, they prove that the residual current \(R_Y\) is intrinsically identified to a canonical element of the infinitesimal cohomology of first order with supports in \(Y\) and with values in the sheaf of sections of the determinant of the determinant of the conormal bundle to \(Y\).