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

Jean Ruppenthal ; Håkan Samuelsson Kalm (Institutionen för matematiska vetenskaper) ; Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik)
Indiana University Mathematics Journal (0022-2518). Vol. 64 (2015), 2, p. 533-558.

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.

CPL Pubid: 167592

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Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)
Institutionen för matematiska vetenskaper, matematik (2005-2016)