Complex hypersurfaces in direct products of Riemann surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866909247518801920 |
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| author | Isenrich, Claudio Llosa |
| author_facet | Isenrich, Claudio Llosa |
| contents | We study smooth complex hypersurfaces in direct products of closed hyperbolic Riemann surfaces and give a classification in terms of their fundamental groups. This answers a question of Delzant and Gromov on subvarieties of products of Riemann surfaces in the smooth codimension one case. We also answer Delzant and Gromov's question of which subgroups of a direct product of surface groups are Kähler for two classes: subgroups of direct products of three surface groups; and subgroups arising as kernel of a homomorphism from the product of surface groups to $\mathbb{Z}^3$. These results will be a consequence of answering the more general question of which subgroups of a direct product of surface groups are the image of a homomorphism, which is induced by a holomorphic map, for the same two classes. This provides new constraints on Kähler groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_02357 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Complex hypersurfaces in direct products of Riemann surfaces Isenrich, Claudio Llosa Geometric Topology Algebraic Geometry Group Theory We study smooth complex hypersurfaces in direct products of closed hyperbolic Riemann surfaces and give a classification in terms of their fundamental groups. This answers a question of Delzant and Gromov on subvarieties of products of Riemann surfaces in the smooth codimension one case. We also answer Delzant and Gromov's question of which subgroups of a direct product of surface groups are Kähler for two classes: subgroups of direct products of three surface groups; and subgroups arising as kernel of a homomorphism from the product of surface groups to $\mathbb{Z}^3$. These results will be a consequence of answering the more general question of which subgroups of a direct product of surface groups are the image of a homomorphism, which is induced by a holomorphic map, for the same two classes. This provides new constraints on Kähler groups. |
| title | Complex hypersurfaces in direct products of Riemann surfaces |
| topic | Geometric Topology Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/1806.02357 |