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• W3100607470 abstract "Let X be a singular Hermitian complex space of pure dimension n. We use a resolution of singularities to give a smooth representation of the L2-∂¯-cohomology of (n,q)-forms on X. The central tool is an L2-resolution for the Grauert–Riemenschneider canonical sheaf KX. As an application, we obtain a Grauert–Riemenschneider-type vanishing theorem for forms with values in almost positive line bundles. If X is a Gorenstein space with canonical singularities, then we also get an L2-representation of the flabby cohomology of the structure sheaf OX. To understand also the L2-∂¯-cohomology of (0,q)-forms on X, we introduce a new kind of canonical sheaf, namely, the canonical sheaf of square-integrable holomorphic n-forms with some (Dirichlet) boundary condition at the singular set of X. If X has only isolated singularities, then we use an L2-resolution for that sheaf and a resolution of singularities to give a smooth representation of the L2-∂¯-cohomology of (0,q)-forms." @default.
• W3100607470 created "2020-11-23" @default.
• W3100607470 creator A5059407425 @default.
• W3100607470 date "2014-12-01" @default.
• W3100607470 modified "2023-09-26" @default.
• W3100607470 title "L2-theory for the ∂¯-operator on compact complex spaces" @default.
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• W3100607470 doi "https://doi.org/10.1215/0012794-2838545" @default.
• W3100607470 hasPublicationYear "2014" @default.
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