Till sidans topp

Sidansvarig: Webbredaktion

Adjunction for the Grauer… - Göteborgs universitet Till startsida
Webbkarta
Till innehåll Läs mer om hur kakor används på gu.se

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

Artikel i vetenskaplig tidskrift
Författare Jean Ruppenthal Håkan Samuelsson Kalm Elizabeth Wulcan Indiana University Mathematics Journal 64 2 533-558 0022-2518 2015 Institutionen för matematiska vetenskaper, matematik 533-558 en arxiv.org/abs/1211.3660 Matematik, Matematisk analys, Geometri

Sammanfattning

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.