Geodesic
Multidimensional residue theory and the logarithmic de Rham complex
Journal of Singularities, Tome 5 (2012), pp. 1-18

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We study logarithmic differential forms with poles along a reducible hypersurface and the multiple residue map with respect to the complete intersection given by its components. Some applications concerning computation of the kernel and image of the residue map and the description of the weight filtration on the logarithmic de Rham complex for hypersurfaces whose irreducible components are defined by a regular sequence of functions are considered. Among other things we give an easy proof of the de Rham theorem (1954) on residues of closed meromorphic differential forms whose polar divisor has rational quadratic singularities, and correct some inaccuracies in its original formulation and later citations. 
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     title = {Multidimensional residue theory and the logarithmic de {Rham} complex},
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A. G. Aleksandrov. Multidimensional residue theory and the logarithmic de Rham complex. Journal of Singularities, Tome 5 (2012), pp. 1-18. doi: 10.5427/jsing.2012.5a

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