Composite residues with determinant denominators

Question

I am looking for a good reference on composite residues of multi-variable contour integrals (something better and more explicit than Griffiths and Harris or Tsikh). This means I want to evaluate $\oint \frac{d^nz}{p(z)}$ where $p(z)$ is a homogeneous degree $n$ polynomial in $n$ variables, and I want the residue at $z = 0$.

I understand that this is a difficult problem in general, but in my particular case one can regard the $z$ variables as entries in a matrix, and $p(z)$ is a product of various minor determinants of this matrix. I know what the answer should be ahead of time, and I know that it's pretty, but I can't prove it, so I'd be interested in references where similar residues have been computed.

Thanks, Jared

Answer 1

I'm not an expert in this area but perhaps "Residue calculus and applications" by M. Elkadi and A. Yger, and the references therein, as well as the "residue form" entry on the Springer Encyclopedia of Mathematics, could help a bit.