# Bubbling complex projective structures with quasi-Fuchsian holonomy

## TL;DR

This paper demonstrates that for a generic complex projective structure with quasi-Fuchsian holonomy on a closed surface, structures with two branch points can be derived from bubbling unbranched structures with the same holonomy.

## Contribution

It establishes a generic bubbling characterization of branched structures with quasi-Fuchsian holonomy on closed surfaces.

## Key findings

- Structures with two branch points are obtained by bubbling unbranched structures.
- Most branched structures with the given holonomy are related through bubbling.
- The result applies to generic cases with quasi-Fuchsian representations.

## Abstract

For a given quasi-Fuchsian representation $\rho:\pi_1(S)\to$ PSL$_2\mathbb{C}$ of the fundamental group of a closed surface $S$ of genus $g\geq 2$, we prove that a generic branched complex projective structure on $S$ with holonomy $\rho$ and two branch points is obtained by bubbling some unbranched structure on $S$ with the same holonomy.