Complex hypersurfaces in direct products of Riemann surfaces

Claudio Llosa Isenrich

doi:10.2140/agt.2024.24.1467

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arXiv · 1806.02357

Complex hypersurfaces in direct products of Riemann surfaces

Claudio Llosa Isenrich

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Abstract

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.

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BibTeX RIS

Claudio Llosa Isenrich. 2021-09-27. Complex hypersurfaces in direct products of Riemann surfaces. https://doi.org/10.2140/agt.2024.24.1467

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