Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L^2-cohomology classes
Rapport, 2012

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.

Författare

Håkan Samuelsson Kalm

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Elizabeth Wulcan

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Jean Ruppenthal

Ämneskategorier

Matematik

Geometri

Matematisk analys