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arXiv · 2008.13106

Uniruledness of some low-dimensional ball quotients

Yota Maeda
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Abstract

We define reflective modular forms on complex balls and use a method of Gritsenko and Hulek to show that some ball quotients of dimensions 3, 4 and 5 are uniruled. We give examples of Hermitian lattices over the rings of integers of imaginary quadratic fields $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$ for which the associated ball quotients are uniruled. Our examples include the moduli space of 8 points on $\mathbb{P}^1$. Moreover, we find that some of their Satake-Baily-Borel compactifications are rationally chain connected modulo certain cusps.

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Yota Maeda. 2020-08-30. Uniruledness of some low-dimensional ball quotients. https://doi.org/10.1007/s10711-023-00844-5

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