Quotients of the holomorphic 2-ball and the turnover

TL;DR

This paper constructs new complex hyperbolic structures on disc orbibundles over the sphere with three cone points, providing flexible examples contrasting previous rigid cases, including structures on trivial and cotangent bundles over Riemann surfaces.

Contribution

It introduces two-dimensional families of complex hyperbolic structures on disc orbibundles, expanding the known examples beyond rigid cases.

Findings

Constructed families of complex hyperbolic structures on orbibundles.

Provided examples on trivial and cotangent bundles over Riemann surfaces.

Contrasted with previously known rigid structures.

Abstract

We construct two-dimensional families of complex hyperbolic structures on disc orbibundles over the sphere with three cone points. This contrasts with the previously known examples of the same type, which are locally rigid. In particular, we obtain examples of complex hyperbolic structures on trivial and cotangent disc bundles over closed Riemann surfaces.