On the \(L^ 2\) cohomology of complex spaces (Q1204262)
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scientific article; zbMATH DE number 126377
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(L^ 2\) cohomology of complex spaces |
scientific article; zbMATH DE number 126377 |
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On the \(L^ 2\) cohomology of complex spaces (English)
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3 March 1993
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Let \(X\) be a reduced complex space of pure dimension \(n\) equipped with a Hermitian metric. It is proved that the \(L^ 2_{\text{loc}}\) (i.e. locally square integrable) de Rham cohomology group of \(X\) is canonically isomorphic to the (middle) intersection cohomology group of \(X\). This settles a question of \textit{J. Cheeger}, \textit{M. Goresky} and \textit{R. MacPherson} [cf. Ann. Math. Stud. 102, 303-340 (1982; Zbl 0503.14008)].
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locally square integrable de Rham cohomology
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reduced complex space
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intersection cohomology
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0.9836712
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0.9452739
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0.9286666
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0.9202808
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0.9189851
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