We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus g≥ 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.
Francaviglia S., Ruffoni L. (2021). Local deformations of branched projective structures: Schiffer variations and the Teichmüller map. GEOMETRIAE DEDICATA, 214(1), 21-48 [10.1007/s10711-021-00601-6].
Local deformations of branched projective structures: Schiffer variations and the Teichmüller map
Francaviglia S.;
2021
Abstract
We study a class of continuous deformations of branched complex projective structures on closed surfaces of genus g≥ 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.| File | Dimensione | Formato | |
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