The linear Shafarevich conjecture for quasiprojective varieties and algebraicity of Shafarevich morphisms
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916374496935936 |
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| author | Bakker, Benjamin Brunebarbe, Yohan Tsimerman, Jacob |
| author_facet | Bakker, Benjamin Brunebarbe, Yohan Tsimerman, Jacob |
| contents | We prove that the universal cover of a normal complex algebraic variety admitting a faithful complex representation of its fundamental group is an analytic Zariski open subset of a holomorphically convex complex space. This is a non-proper version of the Shafarevich conjecture. More generally we define a class of subset of the Betti stack for which the covering space trivializing the corresponding local systems has this property. Secondly, we show that for any complex local system $V$ on a normal complex algebraic variety $X$ there is an algebraic map $f \colon X\to Y$ contracting precisely the subvarieties on which $V$ is isotrivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16441 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The linear Shafarevich conjecture for quasiprojective varieties and algebraicity of Shafarevich morphisms Bakker, Benjamin Brunebarbe, Yohan Tsimerman, Jacob Algebraic Geometry Complex Variables Differential Geometry 14C30, 14D07, 14D20, 14E20, 14F35, 32E05, 32Q30, 32U10, 53C43, 58A14 We prove that the universal cover of a normal complex algebraic variety admitting a faithful complex representation of its fundamental group is an analytic Zariski open subset of a holomorphically convex complex space. This is a non-proper version of the Shafarevich conjecture. More generally we define a class of subset of the Betti stack for which the covering space trivializing the corresponding local systems has this property. Secondly, we show that for any complex local system $V$ on a normal complex algebraic variety $X$ there is an algebraic map $f \colon X\to Y$ contracting precisely the subvarieties on which $V$ is isotrivial. |
| title | The linear Shafarevich conjecture for quasiprojective varieties and algebraicity of Shafarevich morphisms |
| topic | Algebraic Geometry Complex Variables Differential Geometry 14C30, 14D07, 14D20, 14E20, 14F35, 32E05, 32Q30, 32U10, 53C43, 58A14 |
| url | https://arxiv.org/abs/2408.16441 |