Published Paper
Inserted: 21 dec 2019
Last Updated: 1 jun 2022
Journal: Geometriae Dedicata
Year: 2021
Doi: https://doi.org/10.1007/s10711-021-00601-6
Abstract:
We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus $g\geq 2$, which preserve the holonomy representation of the structure and the order of the branch points. In the case of non-elementary holonomy we show that when the underlying complex structure is infinitesimally preserved the branch points are necessarily arranged on a canonical divisor, and we establish a partial converse for hyperelliptic structures.