Uniruledness of some low-dimensional ball quotients

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.

References in corpus (1)

• The Kodaira dimension of the moduli of K3 surfaces

Cited by in corpus (1)

• Reflective obstructions of unitary modular varieties