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Topological invariance of the weight filtration. (English) Zbl 0539.14016

The paper addresses the problem: under which conditions is the weight filtration on the cohomology of a compact complex algebraic variety preserved under homeomorphisms? After a discussion of this question it is shown that the answer is always positive for compact algebraic surfaces (for quasi-projective surfaces the weight filtration is not even an analytic invariant). The proof uses the weight filtration on a neighborhood boundary of the singular locus, as introduced by A. H. Durfee [Duke Math. J. 50, 1017-1040 (1983)] and the topological structure of this 3-manifold [see W. D. Neumann, Trans. Am. Math. Soc. 268, 299-344 (1981)].
In particular, for isolated surface singularities the weight filtration on the cohomology of the link is a topological invariant. For higher dimensional singularities this is no longer true; examples are given of diffeomorphic links with different weight filtration.

MSC:

14F45 Topological properties in algebraic geometry
14F25 Classical real and complex (co)homology in algebraic geometry
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