1,186 research outputs found
A pullback operation on a class of currents
For any holomorphic map between a complex manifold and a
complex Hermitian manifold we extend the pullback from smooth forms
to a class of currents in a cohomologically sound way. We provide a basic
calculus for this pullback. The class of currents we consider contains in
particular the Lelong current of any analytic cycle. Our pullback depends in
general on the Hermitian structure of but coincides with the usual pullback
of currents in case is a submersion. The construction is based on the Gysin
mapping in algebraic geometry.Comment: Theorem 1.2 is improve
Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L2-cohomology classes
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.Comment: 20 page
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