The Penrose transform for compactly supported cohomology
نویسنده
چکیده
Let the manifold X parametrise a family of compact complex submanifolds of the complex (or CR) manifold Z. Under mild conditions the Penrose transform typically provides isomorphisms between a cohomology group of a holomorphic vector bundle V → Z and the kernel of a differential operator between sections of vector bundles over X. When the spaces in question are homogeneous for a group G the Penrose transform provides an intertwining operator between representations. In this paper we develop a Penrose transform for compactly supported cohomology on Z. We provide a number of examples where a compactly supported cohomology group is shown to be isomorphic to the cokernel of a differential operator between compactly supported sections of vector bundles over X. We consider also how the “Serre duality” pairing carries through the transform.
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تاریخ انتشار 2008