Integration Formulae and Kernels in Singular Subvarieties of Cn

The Bochner-Martinelli and Ramirez-Khenkin integration formulae are a pair of cornerstones of the field of several complex variables. They are naturally defined on open domains of C-n. An obvious problem is to produce respective integration formulae on general smooth or singular varieties. We propose in this work a simple technique for producing integration formulae on singular subvarieties defined as the zero locus of special polynomials in C-n. The main idea is to push down the integration kernels from a neighborhood of the subvariety into the subvariety itself.