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 $g\ge 2$, 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.

39 pages, 20 pictures

References in corpus (1)

• Multi(de)grafting quasi-Fuchsian complex projective structures via bubbles

Cited by in corpus (3)

• Local deformations of branched projective structures: Schiffer variations and the Teichmüller map
• Multi(de)grafting quasi-Fuchsian complex projective structures via bubbles
• Tame and relatively elliptic ${\mathbb{CP}}^1$-structures on the thrice-punctured sphere