Bubbling complex projective structures with quasi-Fuchsian holonomy

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.