Residue in intersection homology for quasihomogeneous singularities

Details Residue in intersection homology for quasihomogeneous singularities Residue in intersection homology for quasihomogeneous singularities

1996-11-26

arxiv.org/abs/alg-geom/9611034v1

Mathematics

Algebraic Geometry

8 pages, AMS-tex

Scientific paper

Suppose M is a complex manifold of dimension $n+1$ and K is a hypersurface in M. By Poincar\'e duality we define a residue morphism $res:H^{k+1}(M\setminus K)\longrightarrow H_{2n-k}(K)$ which generalizes the classical Leray residue morphism to cohomology for smooth K. We assume that K has isolated quasihomogeneous singularities. Suppose $\omega$ is a holomorphic form of the type $(n+1,0)$ with the first order pole on K. The purpose of this note is to give a short, self contained proof of a criterion which tells us when the residue of $\omega$ lifts to the intersection homology of K.

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