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Residue forms on singular hypersurfaces | | Andrzej Weber
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27 Dec 2002 | | Subject: | Algebraic Geometry | math.AG | | Abstract: | The purpose of this paper is to point out a relation between the canonical sheaf and the intersection complex of a singular algebraic variety. We focus on the hypersurface case. Let $M$ be a complex manifold, $Xsubset M$ a singular hypersurface. We study residues of top-dimensional meromorphic forms with poles along $X$. Applying resolution of singularities sometimes we are able to construct residue classes either in $L^2$-cohomology of $X$ or in the intersection cohomology. The conditions allowing to construct these classes coincide. They can be formulated in terms of the weight filtration. Finally, provided that these conditions hold, we construct in a canonical way a lift of the residue class to cohomology of $X$. | | Source: | arXiv, math.AG/0301313 | | Services: | Forum | Review | PDF | Favorites | |
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