English

Residue in intersection homology for quasihomogeneous singularities

alg-geom 2008-02-03 v1 Algebraic Geometry

Abstract

Suppose M is a complex manifold of dimension n+1n+1 and K is a hypersurface in M. By Poincar\'e duality we define a residue morphism res:Hk+1(MK)H2nk(K)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 ω\omega is a holomorphic form of the type (n+1,0)(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 ω\omega lifts to the intersection homology of K.

Keywords

Cite

@article{arxiv.alg-geom/9611034,
  title  = {Residue in intersection homology for quasihomogeneous singularities},
  author = {Andrzej Weber},
  journal= {arXiv preprint arXiv:alg-geom/9611034},
  year   = {2008}
}

Comments

8 pages, AMS-tex