Unbranched Riemann domains over Stein spaces and Cartier divisors
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arXiv
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| Format: | Preprint |
| Published: |
2008
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| _version_ | 1866917169040719872 |
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| author | Alaoui, Youssef |
| author_facet | Alaoui, Youssef |
| contents | It is proved that an unbranched Riemann domain $Π: X\rightarrow Y$ over an arbitrary Stein complex space of dimension $n\geq 2$ is Stein if and only if $X$ is cohomologically $2$-complete with respect to the structure sheaf ${\mathcal{O}}_{X}$ and every topologically trivial holomorphic line bundle over $X$ is associated to a Cartier divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0810_0782 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Unbranched Riemann domains over Stein spaces and Cartier divisors Alaoui, Youssef Complex Variables 32E10, 32C25, 32A07, 14C22 It is proved that an unbranched Riemann domain $Π: X\rightarrow Y$ over an arbitrary Stein complex space of dimension $n\geq 2$ is Stein if and only if $X$ is cohomologically $2$-complete with respect to the structure sheaf ${\mathcal{O}}_{X}$ and every topologically trivial holomorphic line bundle over $X$ is associated to a Cartier divisor. |
| title | Unbranched Riemann domains over Stein spaces and Cartier divisors |
| topic | Complex Variables 32E10, 32C25, 32A07, 14C22 |
| url | https://arxiv.org/abs/0810.0782 |