IUMJ

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

Authors: Jean Ruppenthal, Hakan Samuelsson Kalm and Elizabeth Wulcan

Issue: Volume 64 (2015), Issue 2, 533-558

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 $L^2$-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 $M$.