Additive Riemann-Hilbert Problem in Line Bundles over CP1

Author

Roman Dwilewicz, Missouri University of Science and TechnologyFollow

Abstract

In this note we consider ∂̄-problem in line bundles over complex projective space ℂℙ1 and prove that the equation can be solved for (0, 1) forms with compact support. As a consequence, any Cauchy-Riemann function on a compact real hypersurface in such line bundles is a jump of two holomorphic functions defined on the sides of the hypersurface. In particular, the results can be applied to ℂℙ2 since by removing a point from it we get a line bundle over ℂℙ1

Recommended Citation

R. Dwilewicz, "Additive Riemann-Hilbert Problem in Line Bundles over CP1," Canadian Mathematical Bulletin, Canadian Mathematical Society, Jan 2006.

Department(s)

Mathematics and Statistics

Keywords and Phrases

∂̄-problem; cohomology groups; line bundles

International Standard Serial Number (ISSN)

0008-4395

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 Canadian Mathematical Society, All rights reserved.

Publication Date

01 Jan 2006