Additive Riemann--Hilbert Problem in Line Bundles Over $mathbb{CP}^1$

Canadian mathematical bulletin

关键词: $overlinepartial$-problem;    cohomology groups;    line bundles;   

DOI  :  10.4153/CMB-2006-007-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this note we consider $overlinepartial$-problem inline bundles over complex projective space $mathbb{CP}^1$and prove that theequation can be solved for $(0,1)$ forms with compact support. As aconsequence, any Cauchy-Riemann function on a compact real hypersurface insuch line bundles is a jump of two holomorphic functions defined on thesides of the hypersurface. In particular, the results can be applied to$mathbb{CP}^2$ since by removing a point from it we get a line bundle over$mathbb{CP}^1$.

【 授权许可】

Unknown