Additive Riemann-Hilbert Problem in Line Bundles over CP1
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
R. Dwilewicz, "Additive Riemann-Hilbert Problem in Line Bundles over CP1," Canadian Mathematical Bulletin, Canadian Mathematical Society, Jan 2006.
Mathematics and Statistics
Keywords and Phrases
∂̄-problem; cohomology groups; line bundles
Article - Journal
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