The Penrose transform for compactly supported cohomology

2000/12/21 by Toby N Bailey, Toby N. Bailey, Bailey, Toby N +2
Mathematics · #22E46 #32L25 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Representation Theory (math.RT) #math.DG #math.RT #msc:22E46 #msc:32L25

paper · pdf · doi:10.48550/arxiv.math/0012218

arxiv created 2000/12/21 · openalex publication_date 2000/12/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a version of the Penrose transform which relates compactly supported cohomology on a complex or CR manifold Z to kernels and cokernels of differential operators on a parameter space X of compact complex submanifolds of Z.

Related

• The Penrose Transform for Complex Projective Space
• The Penrose Transform in the Split Signature
• The generalized Penrose-Ward transform
• The inverse Penrose transform on Riemannian twistor spaces
• The Penrose transform on conformally Bochner-Kähler manifolds