Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L²-cohomology classes
Artikel i vetenskaplig tidskrift, 2015

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 $L^2$-cohomology classes of $\bar{\partial}$-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 $L^2$-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

Jean Ruppenthal

Bergische Universität Wuppertal

Håkan Samuelsson Kalm

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Elizabeth Wulcan

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Indiana University Mathematics Journal

0022-2518 (ISSN)

Vol. 64 533-558

Ämneskategorier

Matematik

Geometri

Matematisk analys

Fundament

Grundläggande vetenskaper

DOI

10.1512/iumj.2015.64.5493