Geodesic
Additive Riemann–Hilbert Problem in Line Bundles Over CP1
Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 72-81

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DOI

In this note we consider $\bar{\partial }$ -problem in line bundles over complex projective space $\mathbb{C}{{\mathbb{P}}^{1}}$ 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 $\mathbb{C}{{\mathbb{P}}^{2}}$ since by removing a point from it we get a line bundle over $\mathbb{C}{{\mathbb{P}}^{1}}$ .
DOI : 10.4153/CMB-2006-007-7
Mots-clés : 32F20, 14F05, 32C16, ∂̄-problem, cohomology groups, line bundles 
Dwilewicz, Roman J. Additive Riemann–Hilbert Problem in Line Bundles Over CP1. Canadian mathematical bulletin, Tome 49 (2006) no. 1, pp. 72-81. doi: 10.4153/CMB-2006-007-7
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     title = {Additive {Riemann{\textendash}Hilbert} {Problem} in {Line} {Bundles} {Over} {CP1}},
     journal = {Canadian mathematical bulletin},
     pages = {72--81},
     year = {2006},
     volume = {49},
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     doi = {10.4153/CMB-2006-007-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-007-7/}
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