\(L^ 2\)-cohomology of normal algebraic surfaces. I (Q581485)
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scientific article; zbMATH DE number 4019213
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^ 2\)-cohomology of normal algebraic surfaces. I |
scientific article; zbMATH DE number 4019213 |
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\(L^ 2\)-cohomology of normal algebraic surfaces. I (English)
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1985
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The authors show that the \(L^ 2\)-cohomology of the non-singular part of a complex projective surface with the induced Fubini metric is isomorphic to the middle perversity intersection homology. This was conjectured by \textit{J. Cheeger}, \textit{M. Goresky} and \textit{R. MacPherson} [Semin. differ. Geom., Ann. Math. Stud. 102, 303-340 (1982; Zbl 0503.14008)], and is proved using a modification of arguments of \textit{J. Cheeger} [in Geometry of the Laplace operator, Honolulu/Hawaii, Proc. Symp. Pure Math. 36, 91-146 (1980; Zbl 0461.58002)].
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intersection homology
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\(L^ 2\)-cohomology
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Fubini metric
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middle perversity intersection homology
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