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arXiv · 1211.3660

Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L2-cohomology classes

Jean Ruppenthal·Håkan Samuelsson Kalm·Elizabeth Wulcan
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Abstract

In the present paper, we derive an adjunction formula for the Grauert-Riemenschneider canonical sheaf of a singular hypersurface V in a complex manifold M. This adjunction formula is used to study the problem of extending L2-cohomology classes of dbar-closed forms from the singular hypersurface V to the manifold M in the spirit of the Ohsawa-Takegoshi-Manivel extension theorem. We do that by showing that our formulation of the L2-extension problem is invariant under bimeromorphic modifications, so that we can reduce the problem to the smooth case by use of an embedded resolution of V in M. The smooth case has recently been studied by Berndtsson.

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Jean Ruppenthal, Håkan Samuelsson Kalm, Elizabeth Wulcan. 2013-04-08. Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L2-cohomology classes. https://arxiv.org/abs/1211.3660

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