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arXiv · 2112.03131

On the existence of holomorphic curves in compact quotients of $\mathrm{SL}(2,\mathbb C)$

Indranil Biswas·Sorin Dumitrescu·Lynn Heller·Sebastian Heller
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Abstract

We prove the existence of a pair $(\Sigma ,\, \Gamma)$, where $\Sigma$ is a compact Riemann surface with $\text{genus}(\Sigma)\, \geq\, 2$, and $\Gamma\, \subset\, {\mathrm SL}(2, \mathbb C)$ is a cocompact lattice, such that there is a generically injective holomorphic map $\Sigma \, \longrightarrow\, {\mathrm SL}(2, \mathbb C)/\Gamma$. This gives an affirmative answer to a question raised by Huckleberry and Winkelmann \cite{HW} and by Ghys \cite{Gh}.

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Indranil Biswas, Sorin Dumitrescu, Lynn Heller, Sebastian Heller. 2021-12-06. On the existence of holomorphic curves in compact quotients of $\mathrm{SL}(2,\mathbb C)$. https://arxiv.org/abs/2112.03131

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