Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L²-cohomology classes Journal article, 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.

Author

Jean Ruppenthal

Bergische Universität Wuppertal

Håkan Samuelsson Kalm

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Elizabeth Wulcan

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Indiana University Mathematics Journal

0022-2518 (ISSN)

Vol. 64 2 533-558

Subject Categories

Mathematics

Geometry

Mathematical Analysis

Basic sciences

DOI

10.1512/iumj.2015.64.5493